I'm curious to see what happens in a different LAN. I agree with Keith that this looks like something outside the AP, even a DHCP running out of leases or IP addresses could cause this problem.
So if you can, see if you have access to a different LAN somewhere (home/work/neighbor/lab/friend/school) that has DHCP as well, and see if you experience the same symptoms. At least that will give a hint if it is the AP or the network.
Good luck and keep us posted.