If quantum tunneling will cause rigid objects like rocks to rearrange their atoms into a slow-moving liquid-like state in ~10^65 years, could an object delay this fate through time dilation in a low, stable orbit around a black hole?
10^65 years aren't enough for you?*
Yes, for time as experienced by an observer distant from the black hole. An object always experiences its own proper time, however. For another exercise in time dilation, see The Twin Paradox.
*When you start talking about ridiculously long periods of time like that, you have to take into account a lot of things we normally would neglect. Your black hole might emit non-negligible Hawking radiation in that time, protons might be unstable, etc.