So I don't mean to offend, but there have been 2 other posters with key fob problems who later realized they inserted the battery the wrong way. It may be worth double checking the battery orientation.
I had a problem with coin batteries once and discovered I had used a 2016 cell instead of a 2032 cell. I have equipment that uses both types, and had grabbed the wrong type from my drawer of spares.
I started getting "Remote not detected" messages so I swapped out the key fob battery for a new, name-brand one - but it didn't fix the problem. I tried a spare fob, which worked fine, so I knew the issue wasn't with the car. I opened the problem fob, bent the little metal tabs inward a bit so that they'd apply a bit more pressure to the battery, and that solved the problem. Then I put the original battery back in and it's been working fine.
Now I'm suspecting that the spring contacts have always been a bit marginal and this is why I've never seen the "Low Battery" warning. In the past I've always just replaced the battery when I've gotten repeated "Remote Not Detected" messages.