Try cleaning the circuit board with an eraser, especially where the black magnets touch it.

If that don't work, you most likely have a internal short and it's killing the battery. At that point, I'd replace it with a ebay one and visit your dealer for programming.

 

Could it be that you have four button sensors and only three cutouts in your rubber fob. That forth button may be getting activated since there is no cutout for it. Use it without the rubber fob and see if the battery lasts then.