I've never had facilities destroyed. I'm not sure what people do to manage it. I don't use a lot of explosives, but I've used my fair share of blaster bombs in base defense.
My storage unit is virtually always the first facility I build in a base (since it houses tanks, and having tanks near the entrance is great in base defense). Even if it's not the first thing to be built, it's going to be one of the first. So the majority of the base is going to be disconnected from the access lift if it's destroyed (which destroys the entire base if memory serves).
It's only complicated if you choose to make it so. Virtually any functional base needs a storage unit anyway, so if it's destroyed it needs to be rebuilt or the base won't function well anyway. In my own base designs, it being destroyed usually means a near total base loss anyway.
You can gloss things over lorewise by saying you are using portable generators and make-shift solutions untill main power is back online.
If you feel like editing the map, just stick an alien power supply unit somewhere on the top floor.