Problem was in qa-badge-admin.php, line 546:
$temp = qa_db_query_sub(
'SELECT * FROM ^posts'
);
which obviously also selected the posts' content and led to the memory explosion :)
Just replace it by:
// get post data from table posts
$temp = qa_db_query_sub(
'SELECT postid, type, userid, netvotes, parentid, created, views FROM ^posts'
);
Then it works.