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?
I agree. But who makes governments ? People. When people are welcoming to new era of economics then, obviously future will be different. As Bitcoin is SHA256 based highly encrypted block data chain which secured by contributing power for it, this is really backed by proof of Work.
Currently amount required for production of BTC is quite big and equal to current market price of Bitcoin. And in future difficulty, block heights, block size and number of contributors will increase compare to rewards generated by solving blocks. So obviously comparing demand and supply price of Bitcoin will skyrocket.