The entire internet will never go down. The main threat is segmentation of the internet and thus the block chain into competing chains.

The solution is to HAM or shortwave radio the data between segments, and the miners slow down the block period as necessary to accommodate the slower relaying time.

The coin needs a better (more efficient) design than Bitcoin on the way miners aggregate and relay data.

This can probably all be solved once we get serious development back into a coin. Bitcoin development has become rigor mortis.