The next time this happens, please let me know the date/time it occurs. [Mod: No need to report time now, it's automated: Dear Steve, (Forum getting busy signal)]
Whenever I check the server loads, it's always running below 5% of capacity. I don't think it's a hardware issue or a traffic surge -- the hardware we have should be more than adequate even in cases of high traffic. It could be some runaway software program like a stats program that's hogging too many resources.
It looks like this problem started after our host did an OS upgrade on our server, so that's one reason to suspect it's a software issue. I also upgraded WordPress recently, so maybe the new version of WP is causing these surges. Do the server busy messages correspond with the times I post new blog entries, for instance?