The ten year figure on the tritium bulbs is for the half-life, and correspondingly (assuming no phosphour degredation) they're half as bright. Another 10 years, and they're .25 the original brightness. Theoretically it's asymptotic, and it'll never go out!!!
But in seriousness, I've got a Reflex that I think will still be functional at half or quarter brightness. I know many people aren't fans of them, but they still do have the fiber optic aspect for the daytime (supplementable with cyalume sticks), and if things get terribly bad, they're still useable as an OEG. At nighttime just wait until your eyes are dark adapted enough before you wander out.
As for NiMHs, it's a bit optimistic to believe they'll last that long. Usable lifetime for NiMHs in my digital camera is about a year before internal electrolyte degredation takes it to a point where they're no longer usable. With a low-draw device like an EOTech, I could see an extra 4 or 5 years of usable time, but don't think of batteries as infinitely usable. The solar chargers also are hard on batteries; voltage regulation is kind of flaky.
If I had an electronic sight, I would keep around some lithiums in a cool place (btw, don't ever refrigerate batteries; the cold crystallizes the paste electrolyte). NiCads are terrible for any of this.