BOAC, you haven't missed anything. With a radio altimeter inoperative the autopilot will disconnect 2 sec after LOC/GS capture.
Are you are sure you aren't getting mixed up with autothrottle disengagement 2 seconds after touchdown?
BOAC, I am not sure if you are B737 or not, if you are, have you found anything in the manuals regarding the A/T logic of switching from left RA to right RA with a failure?
The above statement is correct. In dual mode the autopilot will disconnect 2 sec after in case RA1 lost. Vice versa you can not engage the second autopilot in case RA1 failed.
I am also searching a clue suggesting that the A/T system was designed to switch to the correct RA in case of false reading. So far nothing... When checking the schematics can not see much in this direction while the above mentioned switching might have been a hidden circuit.