Call me old fashioned but what is it that keeps this perpetual motion machine going? Why is this system not subject to heat death.
I suggest that Roger Penrose (who's published papers with Stephen Hawking and who proposed the idea) has a better understanding of physics than anybody on this forum. However, it's basically about the re-scaling of the phase space of the universe. The metric of the universe at heat death is remarkably similar to that of the big bang, with the exception of the scale factor. If every particle eventually decays into massless particles (this is a conjecture), then there is no way for the universe to keep track of time or space.
Trouble is we need a real life infinity also it may be argued that this order of energy, if enough to start a universe is going to get less and less each universe. However the idea of entropy being probabilistic does raise the intriguing idea that the universe could suffer instantaneous heat death if what you say is true.
Therefore the whole system runs down to heat death. What is heat death anyway? The loss of the ability to do useful work.
I don't see any problem with a real life infinity and you suggested it in the title of this thread. You also seem to be confusing energy with entropy. The energy of the universe will always be the same*. There is no physical reason why entropy can't be reversed to any arbitrary degree, it's just very, very improbable, but given enough time, it will eventually happen, and given an infinite amount of time, it definitely will happen.
It is however true that the universe may suffer an instantaneous heat death, it's also true that, in this scenario,
Boltzmann brains would be far more common than entire universes. Maybe that doesn't matter, though. How would you tell if your life was a series of Boltzmann brains, each thought separated by vast amounts of time?
* Actually energy conservation is problematic in general relativity anyway.