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?
"Maybe an equally good question is: What could end bitcoin? "
May be not only national government regulations can end Bitcoin, though I think it is the biggest obstacle to sort out. Among other reasons I believe there can be a lack of mass and legitimate adoption, or it can lose its value as people will stop believing in it as the source of quick and easy fortune by speculative trading.