The internet will never totally 'go down'.
I think the question you should be asking is: What services can I expect to access after the dung hits the proverbial?
I’m not sure anyone is truly able to guarantee that. Just because it hasn’t to date, that’s not to say it cannot. Networking is incredibly complex, whereas radio is incredibly simple and doesn’t require a bazillion TCP/IP layers, routers, switches et cetera - radio needs none of that nonsense, natural physics is inherently elegant in this respect.
The internet is
literally the outcome of Cold War research into a network that could survive nuclear war. So while it’s true that (simple) radio is very resilient, so is the internet. What makes the internet resilient is that it is distributed. There’s no one control center. There’s no one managing entity. You could lop the internet in half, and each half would continue to be an internet, kinda like a tapeworm.

The technical definition is that the internet is a
network of networks. Each one is fundamentally self-contained except for its “connector” to other networks.
I’d say that if there is a weak point in the modern internet, it’s DNS, because if DNS fails, you can’t find the servers you need, even if they’re still up and running. (This is exactly how Facebook self-immolated recently: it accidentally took down its own DNS, leaving them unable to reach their DNS servers to fix them, because they were themselves only accessible using DNS!

So they had to physically go to the data centers and fix it right on the machines, which (rightfully) requires getting through many layers of physical security.)
Remember also that what people think the internet is varies wildly: end users think it’s the web. But the web is just one service running on the internet. There are dozens of (often silently) user-facing services, and then a bunch of under-the-hood ones only system administrators ever deal with, and then some even deeper under-the-hood services only certain caliber of network admins ever interact with.
In the end, shutting down the internet would be like saying “shutting down all land travel”. Yes, you could take out major highways. And yes, you could bomb a particular area to kingdom come, not even so much as leaving an existing foot path. But you’d never be able to knock out all land travel, because people can walk across fields. The internet is much the same.