Miners earn bitcoin from 2 sources when they find a block. One source is the award. This award is halved periodically so each block is worth fewer and fewer bitcoin. Theoretically, these awards will continue to decrease until the awards are extremely tiny and eventually (A REALLY LONG TIME FROM NOW) the last award will be given and there will be about 21 million bitcoins.
The second source is transaction fees. When you make a transaction (for instance when you buy a flight on Virgin Galactic) you have no guarantee that the rest of the world agrees that you made that transaction until someone finds a block which includes your transaction. You increase the likelihood of your transaction being approved by offering a transaction fee. This incentivizes miners to look for blocks which include your transaction.
Eventually, the awards will be very very small but there will be more transactions and thus more transaction fees available to miners. Thus miners must continue for as long as bitcoin transaction are being made.
The second source is transaction fees. When you make a transaction (for instance when you buy a flight on Virgin Galactic) you have no guarantee that the rest of the world agrees that you made that transaction until someone finds a block which includes your transaction. You increase the likelihood of your transaction being approved by offering a transaction fee. This incentivizes miners to look for blocks which include your transaction.
Eventually, the awards will be very very small but there will be more transactions and thus more transaction fees available to miners. Thus miners must continue for as long as bitcoin transaction are being made.