When Genmay raised the logout time for a few hours as a joke, they got 4296 “active” users.
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At what time? You must have been checking at night (the vast majority of users are in North America), because we regularly get peak weekday counts in the near 700 range, and the forum rarely slows down. The worst we’ve had was a period where about 1000 extra users (giving a total of ~1600) ended up viewing a single thread, at which point people started getting “Load too high” messages and would need to F5 a few times to get the right page.
Specific stats: http://www.nedstatbasic.net/s?tab=1&link=1&id=2271593 (lower than actual due to image blockers, etc.)
Big-boards.com stats (sorry, thought it was .net :smack: ): Posts last week @ Genmay - 121645. The Straight Dope - 28409.
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I wouldn’t be so sure about the load, and certainly not searches. Genmay has no thread subscription or notification capabilities, so the only way I can quickly find replies to my posts is by searching. Of course, that means the search index needs to be pruned every few months, but at least it doesn’t kill the darn server! This seems to be consistent with the troubles experienced by www.hardforum.com, which, for all the administrator’s “it’s a hardware problem” comments, still runs like a dog on their spiffy new server–paid for with user donations, mind you! 
I don’t know what your configuration is, and I’m no vB or SQL expert, but perhaps it’s worth comparing some of the functionality.