I have 2005 V8 and remote fob only works occasionally.. I have to enter using key which sets off alarm until I put key in ignition. Remote will lock car after I’ve driven car and also works if I return within  30-60 minutes. Otherwise it means using key with alarm sounding etc.

I was told there is a small auxiliary battery somewhere under fuse box that needs replacing. Any help would be gratefully accepted.

The driver door module is at fault here. What you need do is remove the DDR and take out the PCB. Then resolder the chips on the board. The soldered legs on the biggest chip have failed due to heat and vibration. You can tell this because the fault is intermittent, not a failure. By a coincidence I have worked on a DDR this week, picture below. It has 60 pins and a fine solder tip is needed. Do this and it will work again.