Keyless Entry works on/off

[AdamE53]

So, I tried doing a little research here first but couldn't find a solution or similar problem.
We have a 2003 BMW X5 with 2 original keys. Brand new battery installed one year ago. Recently, an interior light and dashcam were left on and drained the battery, but not to the point where it wouldn't start (but very close).
Afterwards, my wife (primary driver) informed me that the keyless entry no longer worked. I tried it and confirmed. Performed a key reprogram for both keys and received successful indications from the car. Tried a key and it worked fine for lock/unlock but not the other key. So, we left that one and stayed with the one that worked, but my wife said it works almost every other day. But, trunk release works all the time.
Problem developed when the battery drained low and now only works half the time. What can I look into? What could be causing the keyless entry to work one day but not the next?