Maybe it is time for a new fan. AFCI's include ground fault protection which trips at about 30ma. The fan that old could have defective insulation which would trip the AFCI. Another thing to investigate, if you haven't already, is the possibility of a grounded neutral conductor which will also cause a trip.
Few things are harder to put up with than the annoyance of a good example.
Unless the fan is actually located IN the bedroom ... I don't see where the requirement for the AFCI exists. The code is pretty clear ... every "outlet" ... and a switch is not an outlet.
In a like manner, simply having the fan pull air from the bedroom does not place it 'in' the room. I suppose a bath fan, where the fan is directly mounted to a hole in the ceiling, could be considered 'in' the bedroom. Let there be even a foot of duct, though, and it's not in the bedroom.
Otherwise, I agree that the fan is likely in need of replacement.
the fan is on it's own curcit,it is in the stairway that is in the bedroom. it is not in the attic.it is a 2 speed fan . check out all connection. next step is to see if breaker is bad.are there any exceptions to the arc-fault rule that i have missed?
Since this is an individual circuit it should be pretty easy to diagnose. At the panel (with the breaker off) check for continuity between the ground and neutral when disconnected from the bus. If it is anything but infinity that is probably the trouble (ground neutral short). Work your way back to the motor until you find it. Next step would be to temporarily hook it up to a regular breaker and hang your clamp on across the ground. It should stay zero. If you have something, I would suspect an intermittent grounded motor winding (real ground fault).