Querying Term Posts in Loop

To expand on the answer from @s_ha_dum – you need to modify a few things about your query.

First, use his suggested tax query:

$args = array(
    'post_type' => 'custcpt', 
    'tax_query' => array(
        array(
            'taxonomy' => 'custtax', 
            'field' => 'id',
            'terms' => $cat->term_id,
        )
    ), 
    'order' => 'ASC'
);

Then, modify your code as follows:

$cat_posts = new WP_Query($args);
while ($cat_posts->have_posts()) :
    $cat_posts->the_post(); 
    // Below, when referencing the post variables, must be as $cat_post->post->ID, etc. ?>
    <center><?php get_the_post_thumbnail($cat_post->post->ID, 'thumbnail'); ?></center>
    <br />
    <?php // Below, don't need to pass the post ID into these functions.  ?>
    <a href="https://wordpress.stackexchange.com/questions/119231/<?php get_permalink(); ?>"><?php get_the_title(); ?></a>
                    <br />
                    <br />

        <?php endwhile; ?>
    <?php endif; ?>

Note a few things:

1. You must use while ($cat_posts->have_posts) to iterate over the
   posts.
2. Call cat_posts->the_post() to prepare the data to be displayed in the functions such as get_the_title()
3. When referencing post variables, such as ID, you must do so as $cat_posts->post->ID
4. When calling functions such as get_the_title(), you do not need to pass the ID in.