I create a rule to log by hostname. Add an action to 'Log to File' add your file path and then use the 'Insert Autosplit value' link to select the Hostname variable. You can also do this manually by adding %Hostname to your file name or path.
If you want to keep the log entries set a suitable log rotation. To just see the last time a host checked in set the total number of files to 1 and the max log file size to 2 or 3k. That will only keep a few log entries before rotating and you will always have one file per host with the latest update time.