AirPort opening too many connections

I'm not sure where to post this question exactly, because I'm not sure what could be causing it.

I've been having a problem with my web host lately, DreamHost. At random, my sites would throw HTTP 503 errors only for my IP address. They'd say "Service Temporarily Unavailable" on a white page for me, but it'd work for everyone else. These were permanent until I asked them to restart Apache. Then they'd come back after some light browsing.

I found that if I skipped the AirPort base station and plugged my computer directly in to the modem, this would never happen. The exact error in Apache's log is:

(Wed Nov 10 15:26:07 2010) (error) (client xx.xx.xxx.xx) access to / failed for xx.xx.xxx.xx, reason: Client exceeded concurrent connection limit of 30

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I contacted my web host's support team about this, and they say:

Unfortunately, that specifically points out the router is doing
something weird, and opening up more connections to your site.

I'd imagine that your router may have some sort of download
accelerator? This might open a LOT of connections at once, causing the
problem you're seeing. To be safe, I restarted apache to see if that
helps.

Otherwise, there's not much else we can do here, since it works w/out
the router.

Click to expand...

Does the AirPort base station have any "download accelerator" that could be causing this? Is it something on my MacBook? This didn't start happening til very recently.

Sorry if this sounds unclear.

Thanks!