When I had to deal with a problem like this I found the information from Devel::Leak rather useful. For tracking down objects I hacked up something like this to use to find where I was allocating objects that never went away: 
package Leaker;
use Data::Dumper;
$Data::Dumper::Indent = 1;
%CLASS;

*CORE::GLOBAL::bless = sub {
  my $obj = shift;
  my $class = shift || caller();
  if (exists $CLASS{$obj}) {
    delete $CLASS{$obj};
  }
  $obj = CORE::bless($obj, $class);
  if ($class =~ /ObjClass/ or (caller())[1] =~ /file|names|here/) {
#    print "$obj created\n";
    $CLASS{$obj} = join "\n\t", map {join ":", caller($_)} 1;
  }
  $obj;
};

sub UNIVERSAL::DESTROY {
  my $obj = shift;
  if (exists $CLASS{$obj}) {
#    print "$obj destroyed\n";
    delete $CLASS{$obj};
  }
}

sub Leaked {
  print Dumper(\%CLASS);
}

1;

[download]
It worked for me. That won't work for classes which have a DESTROY method of their own. (You could just choose to replace those methods on the fly with a wrapper, much like Dominus does with Memoize.) That also won't help much if your memory leak is at the C level. (Which it well could be.)

If all else fails you can just restart yourself with: 

exec($0, @ARGV);

[download]
But personally I would be strongly inclined to have the process hold a lock while it is running, and then have a periodic cron job that starts the job if it is not currently running. A big advantage of that approach is that if you have an unexpected shutdown of the process (eg a machine reboot) then nobody has to remember to start your process again. (This is a classic Unix mistake. Someone writes a daemon that is key to their process, launches it, doesn't document, then 6 months later there is a reboot and nobody knows how to get it running again.)

In reply to Re (tilly) 1: any way to control a memory leak by tilly
in thread any way to control a memory leak by rdww

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