What server type is this, shared, VPS or dedicated?
What is your max_connections set to?

I see this is a new forum, and there is basically nothing on it, so you should not get overloaded.

Perhaps read this post, http://ozzmodz.com/showthread.php/50...g-Spam-Is-Over and install the Ban Spiders by User Agent and Hostname or Useragent Registration Ban modifications, to block bad bots and spiders.

Check the access.log to be entirely sure it's a DoS attack.
Also it's odd that your web-server doesn't crash, but your MySQL server does. It's usually the other way around.

If you're entirely sure it's a DoS attack, you can do several things:
1) Find which IP is doing it and block the IP. A DoS attack is 1 IP, a DDoS attack is sent from a bunch of infected hosts.
2) Go to a host which offers DDoS protection. (Expensive)
3) Use Cloudflare and enable "I'm under attack mode" at the security settings. This should eliminate most attacks. Be sure that you only allow connections to your webs-server from Cloudflare its IP's if you do this.

I doubt it is a dos attack hitting the search.php page.

Running a search will require resources and if maxed out, any extra connection will give the max connection error. If your site is even just fairly busy you can get hundreds of these errors once you peak.

Does this happen at the same daily? maybe your site is running a cron task at that time or doing a back up which is also using resources.

If you are on a shared host your host will most likely spot a real ddos attack long before you will. If on a dedicated that is a different problem all together.