If "append" property is set to true, there is no risk of losing log output. When your app start, it will just write to the existing log file.
If you still wish to add a time-stamp to the log files, I'd recommend to sub-class DefaultTimeBasedFileNamingAndTriggeringPolicy overriding the getCurrentPeriodsFileNameWithoutCompressionSuffix() method. See also TimeBasedFileNamingAndTriggeringPolicyBase and TimeBasedFileNamingAndTriggeringPolicyBase.
If you still wish to add a time-stamp to the log files, I'd recommend to sub-class DefaultTimeBasedFileNamingAndTriggeringPolicy overriding the getCurrentPeriodsFileNameWithoutCompressionSuffix() method. See also TimeBasedFileNamingAndTriggeringPolicyBase and TimeBasedFileNamingAndTriggeringPolicyBase.