use alarm function and catch SIG{ALRM} signal

sub some_sub {
  eval {
    local $SIG{ALRM} = sub {die "died in SIG ALRM";};

    alarm(1);

    my $i=0;

    $i++ while 1;

    alarm(0);
  };
  if ($@) {
    if ($@ =~ /died in SIG ALRM/) {
      print "caught\n";
    }
    else {
      print $@;
    }
  }
}
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my $limit = time + 3_600;
my $cnt;
while (1) {
    ++$cnt;
    last if $cnt > 100 || time > $limit;
    # rest of your loop
}
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I just want to be able to set the program to run for a couple of hours (if need be) and then stop.

(additional emphasis by me)

I personally believe that for such prolonged times a solution along the lines of that suggested by L~R is best suited. Playing with alarm as duly suggested by ccn is more important in short lived situations in which finer control over time is needed and/or you need to timeout "no matter what" e.g. when running external processes:

Incidentally, it is worth reminding that for finer control over (not necessarily) short times a precious module would be Time::HiRes, which is in core.

If you're just trying to limit the number of iterations in your loop, something this simple will work:

my $iterations = 60;
while ( something_is_true  and $iterations-- ) {
  do_something();
}
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Deleted everything, since I was just agreeing with L~R. I swear I loaded the tab in the background before he posted and forgot to reload before posting. :-)