Bill G has actually said something fully correct and understood something profound. It must be because it's classical but I have hope it is a start.SideBar:
I don't answer stupid questions directly Bill G because I assume the person asking them will have enough intelligence and logic to work it out, if I show problems with there answer. People should be able realize the logical science answers in there own way not have me preach an answer at them. If I am being honest I really don't care what you believe, it isn't my concern, all I can do is show the problems with a belief
Now there is nothing special about a black hole it is a basic gravitational object and as such it exchanges gravitational energy as does any celestial object.
Other bodies can do all the normal gravitational things with a black hole like orbit it, gravitational sling shot off it and deflect past it. The body itself frame drags if it rotates which Bill G correctly noted radiating energy away.
ALL THOSE INTERACTIONS EXCHANGE GRAVITATIONAL ENERGY WITH THE BLACK HOLE
The only way we even detect a black hole is by noticing that energy it exchanges with other things because we can't see the black hole itself.
Do you see the irony of your suggestion when put that way Dave, you couldn't detect the black hole if it didn't interact.
The interactions are so normal we have big black holes in the middle of most galaxies.
So we can confidently say a black hole will definitely slow down like every other celestial body UNLESS it feeds on more energy that it is losing .... LAW OF CONSERVATION OF ENERGY.
Anyhow we got there in the end and we finally have black holes exchanging energy correctly.
Now if you are really clever and really logical you can see since the black hole is conserving energy with the rest of the universe then it's no different to F=MA going to infinity situation. The singularity predicted by GR must be either impossible (like you can't change direction infinitely fast, it will be truncated by something) or the singularity itself is linked with the rest of the universe in some way and the physics doesn't end there (Wormholes etc).
Either of those two answers is perfectly acceptable and logical and it isn't up to me to preach which is correct. If you were interested in my opinion I am guessing it is truncated most likely by QM but it is just that an opinion not a fact.
Now if you got to there you DEFINITELY CAN'T HAVE BORN RIGID BODIES IN THE MIDDLE OF A BLACK HOLE IN GR.
So you have to choose Dave which is wrong GR or the BORN RIGID BODY you can't have both as you now have the full continuum. I am happy to accept either answer but not both, they are mutually exclusive (which is why it is a definition in SR). So which do you choose?
For me I am going to be completely logical and choose relativity because I can go from inside the atom to inside the black hole with the one same consistent theory. I suspect most logical people will do the same and your convert and uptake rate is going to be very very low but I wish you luck with it all.