WP_Query() and get_posts() can’t handle over a thousand posts?

So I have a search function that just fetch custom posts and return them as a list.

function search() {

   // post query args
    $args = array(
        'post_type' => 'post_type',
        'posts_per_page' => -1,
        'post_status' => 'publish'
    );

    // markup
    $markup = '<ul>';

    //the loop
    $loop = new WP_Query($args);
    while ($loop->have_posts()) {
        $loop->the_post();
        $markup .= '<li></li>';
    } wp_reset_postdata();

    $markup .='</ul>';

    echo $markup;
}

This works with under a hundred posts but with over a thousand posts, it doesn’t. It just throws an error. If I switch to get_posts(), the same thing happens. Is there another way I could this?