Each recursive call to walktree uses the same $children statement handle. So most likely, each time a recursive call re-executes the $children statement, it clobbers whatever was pending for the caller in that statement handle. When the control returns to the caller, there is nothing left to iterate over.
in reply to walking a tree
If you think about how things happen sequentially, walktree only returns once $children->fetchrow fails. Then right after it returns, the first thing the caller tries to do is $children->fetchrow!
To fix this, either make new statement handles within each call to walktree, or else fetch all of the results from the $children query into an array before recursing at all.