Hi any suggestions?:
1998 Buick Century 3.1 105,000 miles. Factory keyless entry, anti theft chip in ignition key, no alarm system.
Owned the car for a year now, came with one key fob. I bought a second new key fob on ebay, right after I got the car. It looks just the same as the other one and synched and both key fobs have been working just great with the vehicle.
Now recently recently the car battery needed replacement, put a new battery in.
Shortly after, both key fobs stopped working at all or intermittently and when working required very close proximity to the car.

Replaced both key fob batteries and cleaned all contacts in key fobs with a damp rag and reassembled. No change.

Re-synched both key fobs to car, using both the technique of holding unlock door button on driver'* door while pressing unlock lock buttons on key fob one at a time till chirps are heard. Also then tried the place key in ignition three times and pressing both unlock lock key fob buttons till chirps heard. Chirps confirmed ok but key fobs still not working most of the time. It'* like the pickup antenna on the car is broken or ....a corroded fuse or...

Any ideas to try? thanks

It sounds like you've been chasing two separate things:

1. They're either synced or they are not synced.

2. Signal levels.

It would appear to me that the received signal level went down as perceived by the receiver. This could be because the fobs are transmitting more quietly, there is more interference, or the antenna/wiring/receiver have been degraded somehow. In your case, it would be a huge coincidence if both fobs had the same exact problem at the same time so I suspect it is the antenna/wiring/receiver. No amount of resyncing will solve this.

Yes it seems to be a receiver problem..
so what is the common cause and fix for this...?

I'd start by digging out the module and checking the connections.

Well what’* it called and where is it located...?
is it the body control module or

Thank you for all the advice.

It seems the problem was radio frequency interference from an optional device:
Since the factory radio is not Bluetooth, we had got this little Bluetooth transmitter device that plugs into the cigarette lighter and transmits music from the phone onto a radio signal the factory radio can tune to.
We found that whenever this device was plugged in, whether on or off, would weaken the signal from the fob to the vehicle!

Thanks again!