If I'm cut off from the internet, I'm also cut off from my favourite people. That's all there is to it.
If I'm cut off from my cell phone, I'm pretty indifferent. I hate phones in general, and only have a cell for emergencies. I'm also on a really cheap Pay As You Go plan, which gives me a convenient excuse not to talk to people for very long in the first place. Most of my favourite people are similar in this regard, so it all works out.