There are several things you can do
VARCHAR(10240) in all Stored Procedures. This will accommodate longer Family Tree Listings. This is vital because
queue_children can grow longer and longer if you have a lopsided tree structure. It also possible that when queue_children was 1024 in length and did not delimit properly, it probably went into some infinite loop trying to terminate properly and never reached the condition when the
LENGTH(queue_children) would be 0.
GROUP_CONCAT()'s maximum length is limited by group_concat_max_len (default is 1024). Try expanding group_concat_max_len to something ridiculously large (5000000000).
Increase your thread_stack, perhaps 512K or 1M. This is needed for Stored Procedures with either recursive operations or, in this case, longer local variables to make room for.