[Disclaimer: I am not a user of SDL and I do not have it installed. The following is untested guesswork (actually, perl -c says "syntax OK", but untested beyond that).]

After looking at your posted code, I had a similar thought to what ++bliako wrote.

I can see that you've copied the code from "[PDF] SDL::Manual": a visual inspection shows no problems there.

Try replacing this entire call:

$app->add_event_handler(sub {
    ...
});
[download]

with

{
    my %paddle_move;
    my $key_joiner;

    BEGIN {
        $key_joiner = '~';
        %paddle_move = (
            SDL_KEYDOWN . $key_joiner . SDLK_UP, -2,
            SDL_KEYDOWN . $key_joiner . SDLK_DOWN, 2,
            SDL_KEYUP . $key_joiner . SDLK_UP, 0,
            SDL_KEYUP . $key_joiner . SDLK_DOWN, 0,
        );
    }

    $app->add_event_handler(sub {
        my $event = shift;
        my $paddle_key = $event->type . $key_joiner . $event->key_sym;

        if (exists $paddle_move{$paddle_key}) {
            $player1->{v_y} = $paddle_move{$paddle_key};
        }
    });
}
[download]

That will set up all of the possible values for $player1->{v_y} once, at compile time. Assigning those values now only requires a single if condition, instead of the multiple if and elsif conditions you currently have.