No rule
explicitly addresses the case of a fallen-off bumper, and so a Q+A entry or blue-box addition would be required in order to enforce consistent management of a situation like this.
With that said, however, I believe that the game manual does provide a fairly solid foundation upon which said judgment can be founded:
Figure 4-3, "BUMPER corner examples" shows a section of bumper clearly labeled as being "NOT A BUMPER". The sole reason given for this is that this section of bumper does not fulfill the requirements for placement with regard to the BUMPER PERIMETER, regardless of whether or not its construction otherwise meets all remaining requirements for a BUMPER.
I contend that the most reasonable interpretation will therefore be that any section of a ROBOT'S BUMPERS that ceases to fulfill the BUMPER rules
during the course of a match is no longer considered a BUMPER, and should therefore be treated as either part of the robot or field debris (depending on whether or not it actually falls off), same as any other broken ROBOT component.