Bitcoin network may not die in the next 100 years, but there will be new innovations that can compete with Bitcoin in the future because no one knows today's young generation can become a scientist who is able to create new, more modern innovations.
I hope so but we can't assure everything as 100 years of existence had something to think about huge changes may happen on the market or there are other innovations that may happen. I know that we are all in wild guessing knowing that we can surely witness what really be going to happen in the future. However, we are still optimistic about its future and that can help to boost the market even to stay more years and the adoption continues.
^ I selectively read those other replies and it seems they were really don't sure of our existent during that year.
For now, I don't bother myself thinking about what will happen in the next 100 years, it gives you a headache, the best thing you can do is to think about how you can accumulate more BTC into your portfolio so that in the following years you will able to get profit, not on the next 100 year.
Nevertheless, as I am thinking my prediction is the same as the BTC price, it is unpredictable.