AppDelegate.swiftのapplication:didFinishLaunchingWithOptions:などでUIApplicationのidleTimerDisabledにtrueを入れてやれば良い。
func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
UIApplication.sharedApplication().idleTimerDisabled = true
return true
}