To "not really want to read in the time every x seconds" sounds like a unnecessary and valueless optimization to me, since you were talking about doing this at most every minute. In addition to that, if you want to use a formatted date -- and by formatted, I mean anything other than a number of seconds -- you have to figure out how to convert a number of seconds into year, month, ..., second.

If you insist:

our $SLEEP_SECS    = 5;    # Wake up every 5 seconds.
our $GET_TIME_SECS = 2*60; # Resync $time every 2 minutes.
my $time = time;
my $sleep_count = 0;
{
   ... do stuff that doesn't take too long ...

   sleep($SLEEP_SECS);
   if (++$sleep_count * $SLEEP_SECS >= $GET_TIME_SECS) {
      $time = time;
      $sleep_count = 0;
   } else {
      $time += $SLEEP_SECS;   
   }

   redo; # loop back to start
}
[download]

That code falls apart if any signals wake up sleep()