The block reward will continue to half in regular intervals during the next decades, while the price of a Bitcoin can't continue to double in regular intervals during the next decades (see: limits of exponential growth, etc.).

This leaves us with two options:

1) Instead of being financed by the block reward miners will require higher mining fees in order to include transactions. With a decreasing block reward those mining fees will eventually approach the actual cost of a transaction (currently: $50).

2) There will be less miners so mining a single block will be cheaper. This will lead to a decreased security of the network and make the network more vulnerable to attacks.