I don't think you're going to find any ships that have any sort of backup for individual cruise rooms. That said, long term power outages aren't necessarily real common on ships, but they do happen. And generally power to rooms is low on the priority for their backup generation compared to other things (like keeping the bridge running). And in extreme cases, it can be like the Carnival Splendor was, where power was out quite a while.

Now, in at least some of those cases, I wouldn't be surprised if the medical offices at least have some other backup systems in place (but don't know), so it might be possible to visit there in an emergency where power was out elsewhere (although it'd likely involve walking down many flights of stairs to get to it).

I'd guess a lot also comes down to whether it's something where'd it'd be ok for power to be out a couple hours, or whether it's critical that there's power all the time overnight. I'm not a doctor, so I'm not even going to try to make a guess on that for something that important.

But like I said, long term power outtages are definitely the rare event, not common, so this may be something you just have to weigh the risks against the rare chance it happens, because I doubt you'll ever get a guarantee from a cruise line that you'll always be able to get to power in some way.