How about catching the SIGCHLD messages and using that as your trigger to start the process again. Something along these lines.

#!/usr/bin/perl -w

use strict;

launch_child();
$SIG{CHLD}=\&launch_child;
sleep 60 while(1);


sub launch_child{
  print "$$ parent spawning a child\n";
  my $pid=fork;
  if(!$pid){
    print "$$ inside the child\n";
    # all the code that does the real work is in here
    # all the other stuff is just a wrapper to keep
    # this bit going
    sleep 60 while(1);
  }
}
[download]

If you really care about your process you'll back this up with some of the methods mentioned above. You may also want to put some checks on to keep the process from thrashing (constantly restarting the process, which immediately dies again, etc...) just in case. This technique does have the nice side-effect that the restarts are nearly instentaneous.