I doubt it will disappear. Let's remember that all coins will be mined in 100 years from now so it will be here for a long time to stay. This was a very well thought thing to do by Satoshi.
Yes, Satoshi's idea of this digital and cryptography based currency does not reside on a single computer. So, no force will disturb it. And as OP is talking about after 10 years, then there will be laws made for them, so it will be not easy for it to disappear.
120 years until all BTC is mined - I don't think there is a motiv to worry. Especially if you consider that as time goes and BTC will be harder to mine it's price will grow.