My two cents. If it is indeed mysql persistence problem, and you decide to disable them, use the following to get the most out of mysql performance.
Configure thread_cache within my.cnf to be just high enough so that threads_created stat line does not increase. You'll have to monitor the mysql server during peak hours to see which value is best.
If you have the above variable set correctly, non-persistent mysql connection will be as fast from php , espeically if using sockets, as compared to persistent ones.
For me personally, using enabling mysql persistence within php had always caused severe scaling problems for me in the past.