That's certainly a possibility.
Terry, can you clarify how often this happens, as 'from time to time' sounded occasional rather than regular to me. Has the car been restored in the past (perhaps by a previous owner - minor parts such as rubber bump stops seem to be overlooked in quite a few restorations) and are the other rubber items on the car in good condition, or cracked/dry rotted, which could lead to them falling off?