Does Bitcoin have a built-in life expectancy? I understand that the supply of Bitcoins, by design, will not continue to grow to infinity, but is "capped" at 21,000,000. This amount is not in circulation, however, because there are coins that have yet to be mined. I also understand that the reward for a successful miner is 25 coins, but that the reward will be reduced by a factor of 0.5 at certain points. It seems like the supply of coins will always approach 21,000,000 but never actually get there - a limit. If this is all accurate (please correct me if it isn't), does this imply that the incentives for miners will also be reduced? As time goes on, following this logic, miners should stop working altogether, at which point, new transactions can no longer be added. 

Assuming this all plays out, would people simply "roll" into a new blockchain at that time?
but never actually get there 


Except at some point there will be a rounding error (as numbers are integers in the code) to zero new coins being mined.


  does this imply that the incentives for miners will also be reduced? 


Not really. First of all the miners also collect all the fees from all transactions. That should compensate for the reduction in new coins being mined. Another factor is the price of Bitcoin, either in USD or by the time USD doesn't exist anymore, the number of aircraft carriers you can buy for 1 Bitcoin.

Rolling out a new chain will actually probably become harder and harder over time as the network effect causes people to use the chain that is most useful. The number of other people that use it is a big part of its usefulness.