Yeah, that's one of the big drawbacks of trying to use crypto when SHTF--if there's no power, there's no way to send it unless you can at least keep your cell phone charged, and even then it's not reliable.
For now. I can imagine a future run on mesh networks instead of centralized ISPs and cell data providers. Portable generators, including increasingly efficient hybrid solar powered ones, are becoming cheaper and more common too.
Bitcoin is problematic in conflict zones and downed electrical grids in these early days, but I believe it will be much sturdier within a decade or two.
If the zombie apocalypse ever hits though (or any other situation where the grid
permanently fails), then Bitcoin is pretty fucked. But then so is the USD or pretty much any form of money. Bullets and food/water would probably become the dominant currencies in that case.
