So you were storing the keyfob far away (perhaps 20+ feet/7 meters) from the other fobs and far away from where you were storing it before? If so, then you might be right about it just being defective
Because it is so expensive and will cost $ also to program, it might be worth a final test. It would REALLY suck to spend hundreds of dollars only to find a new one does the exact same thing. Store the large ACTIVE fob in a closed metal box on the other side of the house or even at work or something. Use only your small PASSIVE fob to start the bike for the next couple of weeks. Then test the active (large) fob again.
I've tested FOB functions, and can say for sure, even if a FOB was stored in the glove box, it is never "pinged" by the system until the Stove Key is depressed.. just doesn't happen, so a FOB near the bike, means nothing as far as battery life.. only time the battery comes into play, is during the normal "press down knob,(system "pings" FOB, and return signal), turn knob, start bike" sequence.. I also can say without a doubt, a FOB, sitting 10 feet (2-1/2 meters) from the bike, will not receive the "ping, and return a signal to start" I sometimes carried my extra fob, inside an Altoids mint tin, in my tank bag, and can say it would not actuate the system when shielded even on the tank,
I'm actually thinking there is some debris inside your FOB, shorting out your battery, and draining it, or, a strange broken connection, allowing a current drain of the FOB batt.. it's all a passive system in whole, and nothing on the bike effects the FOB, till the Stove Knob is pressed.. there might be some vague possibility that something is wonky with the actual ignition switch, where it does not "break the signal after a start/shutdown", and if that is the fact, yes, it would keep "pinging" for a FOB's presence, and the FOB if present withing 6 feet (2 meters), may keep sending a signal.. but that is highly unlikely, and pretty far fetched to see occurring.. kinda like "never seen that before".
Still, really not a big seal, as long as your bike's immobilizer functions were positively set up, and the passive chip / rfid portion functions.. I'd make sure it was done that way, and suggest you pull the batt from your active fob, and follow the "place fob against lock" start to insure it works.