sub slumber {    # signal-safe sleep, added
    my $span = shift;
    $span -= sleep $span while $span > 0;
    1;
}

$SIG{CHLD} = 'IGNORE';

while (1) {
    defined( my $cpid = fork )
        or warn $! and slumber 5 and next;
    slumber 5 and next if $cpid;        # parent
#   $SIG{INT} = $SIG{HUP} = sub {};     # child
    $SIG{INT} = $SIG{HUP} = 'IGNORE';   # child
    exec qw(rsync -a rsync://blah.example.com/foo foo);
    die 'exec failed';
}