I have a Cisco 3560 switch here at home, and in the default config the AP boots and resets too quickly.
By the time the speed negotiation completes, and spanning tree sorts itself out, the AP has already reset, causing it all to happen again.
I had to issue the following to get these AP to work with it:
interface FastEthernet0/44
switchport mode access
speed 100
duplex full
spanning-tree portfast
Once I added those, the switchport lights up quickly, and the AP got online.