• while (1) {}
  is a wasteful way of doing
  sleep while 1;

• You never collect the child processes you create in the outer parent. You'll accumulate zombies and run out of resources.

• Using signals adds fragility, and they're not necessary here.

I'd try the following:

#!/usr/bin/perl

use strict;
use warnings;

use POSIX       qw( _exit );
use Time::HiRes qw( sleep time );  # Optional.

use constant PERIOD => 10.0;

sub tick {
    my $pm = ...;
    ...
}

sub sleep_till {
    my ($sleep_till) = @_;
    for (;;) {
        my $duration = $sleep_till - time();
        last if $duration <= 0;
        sleep($duration);
    }
}

{
    $SIG{CHLD} = 'IGNORE';  # Autoreap children
    my $time = time();

    for (;;) {
        $time += PERIOD;
        sleep_till($time);
        my $pid = fork();
        if (!defined($pid)) {
            warn("fork: $!\n");
        }
        elsif (!$pid) {
            $SIG{CHLD} = 'DEFAULT';
            _exit(0) if eval { tick(); 1 };
            print STDERR $@;
            _exit($! || ($?>>8) || 255);
        }
    }
}
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