Mine did that but it had nothing to do with the key fob.

It was a bad fuse. Sorry I can't recall which fuse but you can try the fuse for the door lock first.

EDIT:
http://www.grandprix.net/ubb/ultimatebb.php?ubb=get_topic;f=1;t=007131;p=1#000001

On my end it was the MAP sensor. When I replaced it, the on/off locking stopped. Note I did have a code but the SES light wasn't on. I knew I had a code only because of the Aeroforce gauge. Your MAP sensor may be bad also. Why the map sensor affected the locks? Either the misinformation from the MAP + tranny position told the computer to unlock thinking it was in park. Dunno.

That's crazy... I have no idea how a MAP sensor could cause that!

yea i'll have to check it out because i left the remote at home... and it still did it... did yours do it all the time or did i just choose when to do ti... mine just does it at random... 10 min it wont 10 min it will... and the interior lights are flashing now... and it sounds like the little click from the turn signal is going off too...

Sorry for the late response.

Mine was completely random. About every 5 to 20 seconds.

Now the interior light flashing, that's different. Click noise? Now I am sensing short. Still recommend getting it scanned.