If it stopped working suddenly, and wasn't dropped or exposed to water, the batteries may need replacing.
Confirm that nothing is blocking the remote signal receptor on the TV, as well.
Amazon's Fire Stick remote app from Google Play is a workaround if you don't wish to purchase a new Fire Stick:
[link|https://play.google.com/store/apps/details?id=com.amazon.storm.lightning.client.aosp|https://play.google.com/store/apps/details?id=com.amazon.storm.lightning.client.aosp|new_window=true]