eval{
  $SIG{ALRM} = sub {die "DING-DING"};
  alarm(10);
  sleep(20); # <-- This line is missing
  print "I am frustrated.";
  alarm(0);
};

##</code><code>##

sub long_running_function {
  ...
  while ($your_condition) {
    ...
    return undef if -f $post_file; # Or die() if you want
    ...
  }
}

unlink $post_file; # May fail silently, but who cares?
...
&long_running_function();
...