Yes, it makes sense. And it is/was the same behaviour here.
fmtx shuts down or better goes into 'sleep mode' after a while of no transmit. If you got an active bt connection paired it will switch to that one (as you described). I did not dig any deeper, but switched to fm-carkit which is one of the best packages for Maemo and imho way better than using a lousy weak low or simply run-out-of-power BT headset.
Worth a shot. Or just shut down your bt headset. You need bt enabled on N900 due to known reason
Other solution I do not know. But if you investigate and come up with another idea ..... we are here.