If your problem is brief brownouts or similar — my experience is that some consumer broadband routers have cheap power supplies that leaves them in bad states when PCs will pull through — you could put them on a UPS.

If your problem is that your router is unstable, you could just replace your router. Like, if you need remote access and you have a flaky router, that seems like a prime choice.

You could have a power control device or something and have another machine on your network set up so that if it loses Internet connectivity for some sustained period of time, it power-cycles the router.

If this is for when you’re a long ways away, do you have a friend who you’d trust with a key and flipping a switch?

I expect that there are business-oriented routers that will have integrated watchdog features that will auto-reboot if they hang. I have not gone looking, though.

Possibly, if it’s compatible with your use case, and uptime is critical enough here, having a second, backup server elsewhere, possibly not self-hosted. I mean, your connectivity is always going to be bounded by the reliability of your residential Internet connection otherwise.