Why they stop?

Because your running too many threads.

And because your code is badly structured. This is an endless loop that does nothing useful.

    while (1) {
        my $url = $task_q->dequeue();
        my $ua = LWP::UserAgent->new(timeout => 3);
        my $res = $ua->request(HEAD $url);
        $result_q->enqueue(
            "$tid;$url;" 
            . $res->code() 
            . ";" 
            . $res->message() 
            . ";"
        );
    }
[download]

All your code does is prove that if you write badly structured code and run gazillions of threads, you can induce non-useful behaviour.

This is the problem, I’m trying to solve...

The solution is simple: Don't do that! Don't run large numbers of threads. Don't run endless, pointless loops within threads.

All the code you have provided this time is a snippet of the same code from your original post, which you already said was test code--which I cannot correct, because it doesn't do anything useful.