Bitcoin relies on the internet, and the power of computers around the world to power the transactions and iner-workings of the BTC. If the internet "goes down", there will be nothing left to power the whole BTC process, causing it to breakdown.
Agreed, Bitcoin and the internet overall are so linked that it's hard to imagine bitcoin continuing effectively without internet, it would be golden for paper money and gold in general since they would become the only universally accepted currencies.