With ANYTHING battery powered, always suspect the batters (power supply) first before trying anything else. Especially if the battery is 5 or so years old. Could just be corrosion between the battery and the contacts making intermittent connection that can cause all sorts of strange things.
It's simple to do, so give it a whirl. I believe they use a CR2032 battery, which you can find anywhere.
You might even want to get some spray electronic contact cleaner and spray the FOB inside too. Helps clean up all contacts and mating surfaces.
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