The problem could be with the vehicle but it's more likely that you have a bad fob and it will need to be replaced. If you have a second fob that does work and this one does not then that does indicate fob failure. If you don't have a second one then what needs to be done is have this fob tested with a key fob tester to see if it is transmitting.
Just thought I would let people know about my wife's 52 plate 1.6 Stilo. About 3 months ago both remote key fobs started playing up and within a week both stopped working..You could only lock the car and immobilize it with the key. Then BANG suddenly both fobs started to work today, remote
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fiat stilo key fob not working