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?
bad development, its like developing for a side or a group which benefits them and give losses to others which will make Bitcoin user become more less.
no one knows precisely when it will happen but it certainly wont happen easily because as long as there are people still using Bitcoin even if it's just 2 or 3 people then Bitcoin still has value. Thats why we dont have to worry about it as long as we still use it and the others do the same thing.