What does Everett Immortality look like in the long term?

The general idea of EI is that there is always some small chance you will survive in any given situation, so there will be some multiverse timelines whose present is the same as your present, but in which you keep on living indefinitely. However, some forms of survival are a lot more likely than others; eg, it's a lot more likely that my cryonically-preserved brain will be scanned and turned into an AI than that a copy of my brain will spontaneously appear out of nothingness. Thus, it makes sense to plan around the most likely sorts of scenarios, and not to bother doing much planning for the least likely ones.

But thinking /very/ long term, to the heat death of the universe... every form of negentropy is going to end up exhausted, with no more energy gradients that life and intelligence could use to survive from; meaning that however extended a life might be, there will be some point at which all of a person's futures eventually fade away...

... or maybe not. Thermodynamic miracles - events violating ordinary statistics - will, on the long term, happen every so often... so might it be possible for some form of life in that era to rely on them as the last available source of negentropy? Which forms of TMs occur most often, that could most reliably be 'fed' from? How often do they occur, compared to the potential stability of patterns of matter-energy at this time-scale?