comment_reply_link() not showing up

You should try to replace

<?php comment_reply_link(); ?>

with:

<?php comment_reply_link( $args ); ?>

and to make sure the $args['depth'] is not zero or greater or equal than the $args['max depth']. There will be no output if that’s not the case.

If that doesn’t work, you could try to add the comment ID or the comment object as the second input parameter to comment_reply_link( $args, $comment ).

Also check if the comments are open.

Update:

If we look at the default callback, we see how the arguments of comment_reply_link() are constructed:

comment_reply_link( array_merge( $args, array(
    'add_below' => $add_below,
    'depth'     => $depth,
    'max_depth' => $args['max_depth'],
    'before'    => '<div class="reply">',
    'after'     => '</div>'
 ) ) );

where we can see how the depth and max_depth are included.