It is going to be hard for miners to keep mining when the block reward is basically zero, as fees will be the only pay they get.
If the value for the fees in each block is good enough, then miners still maintain their incentive to continue to mine blocks.
Things will get interesting when employers set a salary in Bitcoin, and then have a review period to pay their workers fewer Bitcoins if the inflation rate perpetuates to 0.
Luckily we have many alt coins and many perspectives and communities: with atomic swaps between various useful crypto currencies this will mitigate the inflation decrease and reliance on a single currency.
These can all work in parallel and support a new free world.