追記

SlackのKubernetesのjp-usersチャンネルに投稿したところ、nekopさんより下記の助言をいただきました。ありがとうございます！

https://github.com/kubernetes/kubernetes/pull/46371/files
https://github.com/sjenning/kubernetes/blob/2c866a7aaa45dd552df9ea53cc1ca20b0d502a52/pkg/kubelet/prober/worker.go#L227
https://github.com/sjenning/kubernetes/blob/master/pkg/kubelet/prober/worker.go#L243
https://github.com/sjenning/kubernetes/commit/b49e07846f6779fdb35efb33eab5456bb85ec9f8
https://github.com/kubernetes/kubernetes/commit/b49e07846f6779fdb35efb33eab5456bb85ec9f8

「1.11以降では直っているのではないか？」ということなので、実際に1.11で動かしてみました。

環境

minikube v0.28.2
ただし、今回は--kubernetes-versio v1.11.3をつけてバージョンを変更します。
（前回は1.10系）

kubectl version
# Client Version: version.Info{Major:"1", Minor:"11", GitVersion:"v1.11.3", GitCommit:"a4529464e4629c21224b3d52edfe0ea91b072862", GitTreeState:"clean", BuildDate:"2018-09-09T18:02:47Z", GoVersion:"go1.10.3", Compiler:"gc", Platform:"linux/amd64"}
# Server Version: version.Info{Major:"1", Minor:"11", GitVersion:"v1.11.3", GitCommit:"a4529464e4629c21224b3d52edfe0ea91b072862", GitTreeState:"clean", BuildDate:"2018-09-09T17:53:03Z", GoVersion:"go1.10.3", Compiler:"gc", Platform:"linux/amd64"}

1.11.3で起動しているようです。

Deployment.ymlは前回と同じものをそのまま使います。

疎通確認

0s        0s        1         nginx-deployment-54d7b449d9-xwmsf.15588f8e14305452   Pod       spec.containers{nginx}   Normal    Pulled    kubelet, minikube   Container image "nginx:1.7.9" already present on machine
0s        0s        1         nginx-deployment-54d7b449d9-xwmsf.15588f8e24353f4d   Pod       spec.containers{nginx}   Normal    Created   kubelet, minikube   Created container
0s        0s        1         nginx-deployment-54d7b449d9-xwmsf.15588f8e2f30bd16   Pod       spec.containers{nginx}   Normal    Started   kubelet, minikube   Started container
0s        0s        1         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        5s        2         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        10s       3         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        15s       4         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        20s       5         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        0s        1         nginx-deployment-54d7b449d9-xwmsf.15588f9607af13d7   Pod       spec.containers{nginx}   Normal    Killing   kubelet, minikube   Killing container with id docker://nginx:Container failed liveness probe.. Container will be killed and recreated.
0s        34s       2         nginx-deployment-54d7b449d9-xwmsf.15588f8e14305452   Pod       spec.containers{nginx}   Normal    Pulled    kubelet, minikube   Container image "nginx:1.7.9" already present on machine
0s        34s       2         nginx-deployment-54d7b449d9-xwmsf.15588f8e24353f4d   Pod       spec.containers{nginx}   Normal    Created   kubelet, minikube   Created container
0s        34s       2         nginx-deployment-54d7b449d9-xwmsf.15588f8e2f30bd16   Pod       spec.containers{nginx}   Normal    Started   kubelet, minikube   Started container
0s        35s       6         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        40s       7         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        45s       8         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        50s       9         nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        55s       10        nginx-deployment-54d7b449d9-xwmsf.15588f91418ce085   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        35s       2         nginx-deployment-54d7b449d9-xwmsf.15588f9607af13d7   Pod       spec.containers{nginx}   Normal    Killing   kubelet, minikube   Killing container with id docker://nginx:Container failed liveness probe.. Container will be killed and recreated.
0s        1m        3         nginx-deployment-54d7b449d9-xwmsf.15588f8e14305452   Pod       spec.containers{nginx}   Normal    Pulled    kubelet, minikube   Container image "nginx:1.7.9" already present on machine

2回目のLiveness Probeのチェックも想定通り5回出ていました。
nekopさんご指摘の通りの結果となりました！

まとめ

1.10系での2回目移行のfailureThresholdが1回分少ないのは不具合
v1.11系で修正済み

「多分不具合じゃなくてそういうものなんだろうな」と思ってしまっていたのですが、自分でもよく調べないとダメですね……。
どのコンポーネントが影響していそうかは、なんとなくわかるようにならないといけないと感じました。
（少しずつでもソースに触れないと…。）

旧記事[調査中] KubernetesのLiveness ProbeのfailureThreshold

はじめに

KubernetesのヘルスチェックのfailureThresholdの挙動確認時、自分の想定と異なっていたのでメモ
初回のfailureThresholdは指定値でコンテナ再起動を行うが、再起動後はfailureThreshold-1回で再起動を行うような挙動に見える。

疎通環境

minikube v0.28.2

Deployment
存在しないパスに5秒間隔でヘルスチェックを行い、わざと失敗させる。

apiVersion: apps/v1
kind: Deployment
metadata:
  name: nginx-deployment
  labels:
    app: nginx
spec:
  replicas: 1
  selector:
    matchLabels:
      app: nginx
  template:
    metadata:
      labels:
        app: nginx
    spec:
      containers:
      - name: nginx
        image: nginx:1.7.9
        ports:
        - containerPort: 80
        livenessProbe:
          httpGet:
            path: /pathnotfound # 存在しないパスのため404
            port: 80
          initialDelaySeconds: 10
          periodSeconds: 5
          failureThreshold: 5

想定していた挙動と実際の挙動

想定していた動き

[Created container]
[Started container]
[Unhealthy(1回目)]
[Unhealthy(2回目)]
[Unhealthy(3回目)]
[Unhealthy(4回目)]
[Unhealthy(5回目)]（failureThreshold）
[Kill Container]
[Created container]
[Started container]
[Unhealthy(6回目)]
[Unhealthy(7回目)]
[Unhealthy(8回目)]
[Unhealthy(9回目)]
[Unhealthy(10回目)]（failureThreshold）
[kill Container]
...

実際の動き

[Created container]
[Started container]
[Unhealthy(1回目)]
[Unhealthy(2回目)]
[Unhealthy(3回目)]
[Unhealthy(4回目)]
[Unhealthy(5回目)]（failureThreshold）OK
[Kill Container]
[Created container]
[Started container]
[Unhealthy(6回目)]
[Unhealthy(7回目)]
[Unhealthy(8回目)]
[Unhealthy(9回目)]（failureThreshold?）想定と異なる部分
[kill Container]
...

kubectl get eventの結果

0s        0s        1         nginx-deployment-5cdfc956db-n56dj.155845c2e184ea50   Pod       spec.containers{nginx}   Normal    Pulled    kubelet, minikube   Container image "nginx:1.7.9" already present on machine
0s        0s        1         nginx-deployment-5cdfc956db-n56dj.155845c2edc3eb4f   Pod       spec.containers{nginx}   Normal    Created   kubelet, minikube   Created container
0s        0s        1         nginx-deployment-5cdfc956db-n56dj.155845c2fa234bdc   Pod       spec.containers{nginx}   Normal    Started   kubelet, minikube   Started container
0s        0s        1         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        5s        2         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        10s       3         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        15s       4         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        20s       5         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        0s        1         nginx-deployment-5cdfc956db-n56dj.155845cadd2a06c2   Pod       spec.containers{nginx}   Normal    Killing   kubelet, minikube   Killing container with id docker://nginx:Container failed liveness probe.. Container will be killed and recreated.
0s        34s       2         nginx-deployment-5cdfc956db-n56dj.155845c2e184ea50   Pod       spec.containers{nginx}   Normal    Pulled    kubelet, minikube   Container image "nginx:1.7.9" already present on machine
0s        34s       2         nginx-deployment-5cdfc956db-n56dj.155845c2edc3eb4f   Pod       spec.containers{nginx}   Normal    Created   kubelet, minikube   Created container
0s        34s       2         nginx-deployment-5cdfc956db-n56dj.155845c2fa234bdc   Pod       spec.containers{nginx}   Normal    Started   kubelet, minikube   Started container
0s        35s       6         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        40s       7         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        45s       8         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        50s       9         nginx-deployment-5cdfc956db-n56dj.155845c618efd412   Pod       spec.containers{nginx}   Warning   Unhealthy   kubelet, minikube   Liveness probe failed: HTTP probe failed with statuscode: 404
0s        30s       2         nginx-deployment-5cdfc956db-n56dj.155845cadd2a06c2   Pod       spec.containers{nginx}   Normal    Killing   kubelet, minikube   Killing container with id docker://nginx:Container failed liveness probe.. Container will be killed and recreated.
0s        1m        3         nginx-deployment-5cdfc956db-n56dj.155845c2e184ea50   Pod       spec.containers{nginx}   Normal    Pulled    kubelet, minikube   Container image "nginx:1.7.9" already present on machine