My SE has the same problem. I ended up running a new wire directly from the battery (with a fuse holder) to the battery power for the radio. I've never been able to find the battery wire for the radio, the one that powers the memory.
You can run a wire from the fuse box for the main power for the radio so that it functions as it should on the accessory circuit. What looks like half a fuse holder is a blade terminal socket. Just plug a male blade terminal in where it says "RADIO" next a half-fuse socket.
At one point I had run a wire from the lighter socket to the memory power for the radio. That worked for about a week. Then it shorted out, blew the fuse, and never worked again.
Some people said the lighter socket itself is the culprit and should be replaced. I disconnected my wire from the socket thinking that was the problem, but it didn't help. Putting a new fuse in just wastes another fuse. The Ogre has a page related to this under ghost power or something like that.
It would be nice to know what's going on...
[This message has been edited by 85 SE VIN 9 (edited 07-29-2013).]