Howdy, I don't have a answer to your problem because I have the same problem with my remote. I have changed batteries twice and clean the inside at least twice with electric type contact cleaner used for tv, radios, etc. Like you said this only works for maybe a few weeks. Also I have stood in different places around the car to see if this made any different. This did not help at all. I have found it alway works on the drivers door but about 50% on the other three doors. After either hitting the button two or three or more times does it finally unlock the all doors.
As far as getting a remote you will have to take it to a dealer to have it reprogrammed. Ebay might have new or used remotes. Also if you have the memory driver option on your car make sure you get the correct remotes. Memory option remotes have a 1 or a 2 stamped on the backside. I think the dealer charges maybe on average of $50.00 for reprogramming.
I hope someone might have a better answer on how to repair the remote then spending the money for a new remote and programming. Any out have any more ideas.