I would recommend SEC. You can use SEC to monitor the logfile in real time and have it keep track of what you want it to. You would want a PairWithWindow type rule. Something like this:
action=logonly; pipe '$0' /bin/mailx -s 'MyApplication hasn't stopped in 30 minutes' firstname.lastname@example.org
That rule will send you an email if the app stop isn’t noticed 30 mins after the app start. You would launch sec.pl with the
-input=/path/to/logfile option for it to follow a certain log.