The method Anki uses to send the deck list to the web toolkit can’t cope with very large deck lists. This may be fixed in the future when a different approach is taken, but for now I’m afraid the only option is to reduce the number of decks and/or the length of the names until it starts working again. You could either split unused decks off into a separate profile with export+delete+import, or merge the child decks using https://ankiweb.net/shared/info/113367344