I have a WordPress 3.5.1 site that's getting a little bit of traffic (80 concurrent visitors, ~5 clicks/pageviews per second). The site runs fine until it spikes to ~85 visitors. There are usually 4 admins logged in at the same time. The site has 8 custom post types--Posts has 3500 posts, and Press Releases (a custom post type) has 13000 posts. All of this is paginated on the site, so there are never more than 20 posts showing on any one page.
The only plugins I'm using are wp-pagenavi and w3totalcache.
I set WP_DEBUG_LOG to true and logged the errors. The main error I'm getting (besides various notices and warnings unrelated to this issue) is mysql has reached the max_user_connections limit.
My current max_user_connections is set to 75. I tried to set it higher, but the cpu can't handle the load (4 Quad Core CPUs at 2.17GHz each and 4GB of RAM).
What could be causing so many connections?
I've viewed the mysql processes running when the errors happened and there are many connections that say "SLEEPING" or "SLEEP" (probably 15-20). I also noticed via the process logs that httpd is restarting quite often during the peak traffic times.
Any ideas on how to resolve the issue?
NOTE: Please do not respond if your answer is to check my wp-config.php file and make sure my username, password, and host are correct. This is NOT the issue. The site works fine under normal traffic.