Download KisMac on the Mac Mini, or if it is running Tiger, the Air Traffic Control widget. See what channels your neighbors are running on and see if changing helps.

My friend recently moved into an area with lots of wireless neighbors. His connection worked ok until he had me and another friend over with our laptops. Same symptoms as you described, wireless dropped down from 54 to 11, then lower until we got disconnected. Rebooting the access point (A Belkin one, he and I don't trust Linksys) fixed it for a short time, then it happened again. He changed the channel and enabled SSID broadcast, and things worked great after that.

Keep in mind the only non overlapping channels in the US are 1, 6, and 11. Try to go with an unused channel on one of thise. If not possible, experiment with the others, but keep in mind they will pick up inteference from channels near them.