I'll list some my thoughts about your problem.
- check mysql slow queries log
- or check the number of your queries per request using Zend_Db_Profiler (not accurate work with Zend_Db_* classes can produce a plenty of queries);
- cache metadata;
- increase max_user_connections (about 1000 should be OK, I think).

Just a few ideas that came to my mind at once. If they won't help we'll try to think more