As long as they have live sports rights, they'll stay afloat. There's a reason why networks overpay for those rights. There's a lot of value there. For the most part, people still want to see their sports in real time. Also, networks often use things like NFL telecasts to promote other networking.
The interesting thing will be when a lot of those live sports contracts are up. Mostly in the 2020s. Are you going to see the Amazons, Netflixs, & Googles of the world making a more active approach to gobbling up those rights? You've already seen Twitter dip their toes in. If so, ESPN could be in very deep trouble.