By design, they will stop being produced. That's what the protocol says.

Or rather they'll be produced indefinitely but because the block reward is halved roughly once every four years, it won't be until far into the future till the reward halves from 1 satoshi (0.00000001) to no reward at all because bitcoin is only divisable to 8 places.

So while technically they'll be produced for a long time to go, in practice the reward will be so small miners will be paid through transaction fees instead.