What version of code are you running? And is this just one controller? Some others recently had code issues where APs didn't show in the database. See this thread.
http://community.arubanetworks.com/t5/ArubaOS-and-Mobility-Controllers/Access-Point-shows-down-on-master-up-on-local/td-p/68564
There used to be a "serial over ethernet" feature in the old days, but we don't have it anymore sadly. To use it, the AP had to be connected directly to a controller ethernet port. In the past, I've dug out an old 2400 controller, patched it to the AP at ground level to achieve what you're talking about that.
There's probably another easier way to sort this out though. Two options jump into my mind.
1. If the trouble AP is pingable from the controller, and there's definately no configuration in it's group that's causing the issue, do you have licenses to allow it to connect? You're not at capacity I assume? If not, check the "show datapath session table" to look for the real tunnel session from that AP source IP.
2. If that doesn't tell you what the problem is, can you mirror and sniff the switch port to which the AP attaches? In the past I've found by doing this I can look at the IP destinations and protocols the AP is talking to. This usually gives great info in determining what's going wrong.
Good luck.