aside form a bad fob or bad battery there could be some other interference making your battery drain faster than it should. FOB batteries should last years.

do you keep your FOB on a wall hook or very close to the vehicle when not in use. ie. vehicle parked in garage, FOB hung on a hook near the garage door only a few feet away?

do you carry your keys along with your phone in the same pocket / bag. or near any magnets? in a world with so much tech I wouldn't be surprised if something else was causing the FOB to beacon when not near the car, perhaps something that transmits in the same frequency as a the vehicle maybe

a working FOB battery should last a few years under normal use. my FOB battery lasted 8 years. I also store my FOBs in a faraday box when not in use as well (get one of these if you dont have one)