It seems incredible, but there is a lithium battery in the Kenwood TS570 that apparently lasts about 6 months. Replacing it is a major trip into the innards of your radio.
Clif of AVVID (a Kenwood Service center) was kind enough to tell me what to do, and I thought I would write up his instructions and my experience in case someone else needs it.
According to Clif, the microprocessor must reset correctly or the battery will drain quickly. Therefore you must follow these instructions, as odd as they seem.
Before you begin, you need the radio on a nonconductive surface, a Phillips screwdriver and a CR2032 battery (Radio Shack has them). You also need the radio's power supply hooked up.
That's it! According to Clif the problem won't reoccur. We'll see! Just be careful when you attempt this. Lots of things can go wrong. The case is very tight fitting, so don't drop the pieces and bend them out of shape or you will be sorry. Good luck!
As of March 29th, my battery failed again (yep, about 6 months). I have a month left on my warrantee, so I'm planning on trying to get something resolved. I'll post here about what I find out.
Kenwood did in fact take the Radio back and apparently installed a diode at no charge. With any luck, this will fix the problem. (As of August 1999, so far so good!)