Here is some common problems while using Amazon Fire TV remotes. First question is about a user submitted on Reddit.

I just booted up my fire TV after 1 week and now the remote is not being detected by the fire TV. I pressed the play and select button for 5 secs and still not change.
Amazon_Fire_TV_Remote_Not_Working

Try these

Batteries seem to be the biggest issue I’ve heard so far. Ensure that your batteries are not dead.

If you have more than seven connected remotes or actively connected Bluetooth devices, turn one off.

Ensure that do not place Amazon Fire TV in a cabinet. It could impact your signal strength.

Restart your Amazon Fire TV device. Disconnect the power cord from your Amazon Fire TV device.

Sometimes it takes multiple button presses before the remote is recognized.

A lot of users complained that Amazon Fire TV Remote is a massive battery drainer. Ensure your Bluetooth controller on the Amazon device hasn’t died. The remote could die sometimes. Contact Amazon, they will send you a replacement remote.