Nothing happens to it. Its just like saying what happens to my favourite game show when power goes out. Nothing.
Your bitcoin will still be where you left it, just that you can't access it.
If things are so bad that the internet goes down, your bitcoins is the last thing you will be worried about...
If internet went down, your Bitcoin would still in your wallet but how you can take it out? Everything will be in uncontrol situation. "Bitcoiners" will turn into crazy for sure. The digital currency market will be paralyzed. However, the point is Internet won't down and it will never happen. Just relax and keep investing