If we assume that the two systems are in the same region and that the clocks of these systems are at least set on the same day (hope so!!) and if we also assume that the seconds don't matter, you just need to do your calculations based on hours and minutes. I know that won't work around midnight, so just set a cron to run that anytime elese than around midnight.
I ignore how you'll get the time from both systems (ftp file, remsh, your logs names, etc), but I'd do the following arithmetic from both systems timestamps (ksh syntax):
(( minutes1=`date +"%H"`*60 + `date +"%M"` )) #system 1
(( minutes2=`date +"%H"`*60 + `date +"%M"` )) #system 2
(( minutesDiff=$minutes2-$minutes1 ))
if [ $minutesDiff > 30 ]
then
# do your stuff here
fi
Hope it'll point you to the right direction...