One of the worst things is that it has an element of randomness; there seems no logic to when it will happen. Some days it won't happen at all.. others (usually when there is a podcast I really want to listen to) it will kick in almost immediately. The constant 'kerchink-flip-kerchunk-flop" is unbelievably annoying. After ripping the thing out of the tape deck and smashing it against the dash several times didn't fix it, I tried to find a solution on the internet. I discovered that this was a VERY common occurrence. It even seemed like all adapters, no matter how expensive, would eventually end up doing the auto-reverse flip-flop.
Anyway I did learn of an easy way to solve it. I found this solution in more than one internet forum but there were never any pictures to show you how, so I thought it would be worth an Instructable. It's really easy to do.. all you need is a screwdriver.
Step 1: Dismantle
WARNING: When you open it up all of the component will become "loose" inside because the top of the case is no longer holding them down. Try to identify which half of the case is the "lid" and which half has the spindles for the gears etc. Take the lid side off GENTLY otherwise the bits will fly everywhere and you'll be buggered. If that happens you could try and piece it back together from the photos, but there's no guarantee they'd be the same. Mine is a Digitor brand (on a par with Panaphonics and Sorny I think).
Step 2: Identify trouble-maker
Step 3: Remove trouble-maker
Be careful not to disturb the other stuff in there, or if you do, put it back where you found it! All the other bits are necessary!
It might be worth memorizing where the bits go (or take a photo) before you start fiddling with it. But if you're like me you will realize this after you have dropped it and spread the gears all over the floor.
Step 4: Success!!
Success!! Get ready for some trouble-free listening!
Plug it in and hopefully you should have no more problems with the auto-reverse flip-flop. I read that some people reported the noise from the gears got a bit louder after doing this but personally mine sounded exactly the same as before.