You mentioned you are using a custom taxonomy – therefore including the cat
key in your wp_query args won’t work. wp_query expects that to be the ID of a term belonging to the standard WP category taxonomy. With a custom tax you need to use the dedicated taxonomy parameters.
So your args should be something like:
$post_args = array(
'post_type' => 'donor',
'orderby' => 'post_date',
'posts_per_page'=> '-1', // overrides posts per page in theme settings
'tax_query' => array(
array(
'taxonomy' => 'donor_taxonomy',
'field' => 'term_id',
'terms' => $category->term_id,
),
)
);