This is a bit a bit of a weird question. Simply put, if a body orbits something such as a black hole there is no internal issue (that I know of) that would cause it to eventually stop (by internal I mean that an external force can't be applied as an example). I'm assuming the reason this 'perpetual motion machine' fails is one of the following:
The laws of thermodynamics do factor in external issues (because those laws are what prevents perpetual motion)
This would only work if every object could maintain their gravity (proton decay, hawking radiation etc would pretty much decay the system) and the laws of physics say that they cannot.
To reiterate because see this a lot: I'm not asking if this is a perpetual motion machine, I'm asking why it isn't.