デフォルトでは、Liberty始動時に古いmessages.logとtrace.logファイルはローテートされます。
bootstrap.propertiesファイルに com.ibm.ws.logging.newLogsOnStart=false を設定すると、始動時にローテートされず、古いファイルに追記されます。

参考文書

Log and trace configuration :: Open Liberty Docs
com.ibm.ws.logging.newLogsOnStart
If this setting is set to true when Open Liberty starts, any existing messages.log or trace.log files are rolled over and logging writes to a new messages.log or trace.log file. If this setting is set to false, messages.log or trace.log files only refresh when they hit the size that is specified by the maxFileSize attribute. The default value is true. This setting cannot be provided using the logging element in the server.xml file because it is only processed during server bootstrap.
Maximise log history on Open Liberty in production - OpenLiberty.io.
You can disable this default behaviour in production by adding the new option com.ibm.ws.logging.newLogsOnStart=false on a separate line in a bootstrap.properties file
IBM WebSphere Application Server Performance Cookbook - WebSphere Liberty
On server startup, any old messages.log is first rotated (unless the bootstrap property com.ibm.ws.logging.newLogsOnStart=false is set).