After Hurricane Sandy, cell phone networks in the affected areas were, by and large, not working. Like the situation after Hurricane Katrina, many cell tower sites had no long term back up power source (i.e. a generator), fuel to keep generators running was not available, or generators were flooded out because they were installed on the ground. In the New Orleans area, it was not the storm that took out networks, it was the flooding. As flood waters rose, the high water drowned the generators, power failed, and the networks went down.
This is not rocket science. Fiber and wireless networks can be engineered to be as reliable in a natural disaster as the old telephone network, but it requires spending money in the right places at the right time (i.e. before the disaster).