Well, I spent this weekend trying to figure out what was causing this. The card's rated at a maximum of 18 dBm at 6 megabits according to the datasheet (so, about 63 mW, according to this calculator). Unfortunately, it doesn't list what power output it has on lower modes. I tried turning down the power anyway (to about 60%), but unfortunately it didn't seem to help.
I did some more searching and found a Google cache of this post from the now-closed 1.2.1 RC forum of somebody having a similar issue and it seems like it could be a FreeBSD 7 issue. I tried reverting to 1.2, but it didn't help much. I could load YouTube, which gave me a connection error before, but I couldn't actually play more than a few seconds of any video. So, if it is a FreeBSD issue, it's one that was somehow missed in 6.2 and 7.0.
Just to make sure it wasn't the iPod itself, I pulled out my old WRT54G and turned it into an access point. It works just fine. So, I've got a solution for now, but I'm going to continue to try to find out more information about what might be happening, as I'd really like to use my pfSense unit as the AP instead of having a separate one.
I'll look into whether it might be the power supply. I didn't think of that possibility. It'd be nice if I could just replace that, as it can't be very expensive.