The only honest answer is: for as long as two people or more believe Bitcoin has use and value.
The schedule for block rewards is set to extend out to the year 2130 so bitcoin mining (in its true sense) can continue for that long as long as there are transactions to produce work for.
Maybe an equally good question is: what could end bitcoin? If we think about it from that perspective we can identify what threats exist to seriously harm bitcoin.
One such risk is Governments. They can ban the use of bitcoin among retailers which would seriously diminish the opportunity for adoption growth.
What else?
Short answer; no one knows about bitcoin in the future.
Yes, bitcoin worth because people really think it's worth something. As long as people could buy-sell bitcoin or use it across the world, bitcoin won't vanish or worthless.
There are few countries already banned bitcoin, but more will follow due to illegal funding or anything about illegal activities. But, bitcoin price will not crush just because some countries ban bitcoin, due to bitcoin trading volume spread widely, and most of them are in US, China, Japan, South Korea, HongKong, every country which has bigger exchanges.
What else? Nuclear war, could damage all electronic devices, if it dropped on exchanges locations, just imagine what will happen next.