So the grid goes down and maybe a few have generators, but those run only as long as you have fuel. Batteries salvaged from cars will eventually give out. So you're down to solar and wind, which as we know are notoriously unreliable, but may provide sporadic communications if you can rig up an inverter and some kind of charging system. But eventually batteries won't hold a charge and so you'll have to run your radios directly from the source. Pumped storage may be an option if you have land and the topography to set up a reasonable sized (i.e., pretty big) reservoir.
My guess is most communications in the post-meltdown world will be "lip radio". Not much news from the outside world, IOW.
When we lose power or when we do extended camping, we get by pretty well with a solar panel connected to a deep cell battery. It won’t run a fridge or AC or anything big, but it will charge a laptop, cellphone, walkie talkies, and/or run a low energy LCD TV.
It might work for something like this.
“But eventually batteries won’t hold a charge”
.
The solution to that problem is simple: Desulphators.
They can be had on Ebay for about $35.