Ah… so I googled this problem and saw that there were others out there with the same issue, but nobody ever reported a fix.
The issue: I installed OpenElec on the Rpi2, and it never booted. It would boot once, and look great, then it would reset, announce it was resizing the SD Card (or something like that… I’m working from memory) and that would be that.
The solution: I switched to the latest version! Seems quite obvious writing it down, but the ‘stable’ version didn’t work and the beta did. This was v5.0.8, so this might not be an issue for anybody anymore.
But, it’s a good thing to remember in the future. If at first you don’t succeed, try the previous or the next version. Chances are it isn’t you that’s the problem, and if it is… well, you can always try again.
Curiously, this problem didn’t exist for the first generation Pi (as I tried that, too.)