There was a post describing the 'system has reached maximum resources' message. I found it to occur after simply performing a search in the search box towards the top. Haven't tried the search menu item..
I don't know what you all have as far as a team of technicians or programmers or network admins... However I am a php guru who could help if you need it. I would assume since this site is in php that it's hosted, so I don't know what kind of budget you have for running the site. I would suggest if it's not on a dedicated server to get on one, if it is already on one it seems as though it would require more resources..
If you can't allocate more resources then maybe you can get around that through more efficient designs around things that are creating your bottleneck. I can't, however, analyze your ip packets to make sure you're not a spam target; but could, however, help you design a system that prevents DDoS and such from harming your site much...
let me know if you need any assistance in resolving this issue. It was reported several times even tonight..