Check the battery voltage. It's a 3v Lithium C2032 battery. If it's reading less than 2.8 or so volts, then it's on it's way out. New batteries are about $4 usually, and easy to put in. Just remember that when you put the new battery in, you have to press and hold the lock and unlock buttons next to the car until the horn beeps, before you can use it.
I'm not so sure that it is a battery problem, because my other key fob is also doing it. Are u saying that there is a battery inside the Fob?? I wouldn't mind switching them out and trying. And u say it is safe to do this, that just holding lock/unlock will make it usable?? I have found nothing on this in the manual....n eh