Fees are still not near dominating the rewards so we do expect to see miner revenue drop due to this.
First thing, even if the block reward is zero, there are still transactions fees. We are not here yet but they are expected to be the primary motivation in the future.
Second, difficulty scale proportionally to the global mining power so that one block is mined every 10 minutes or so. As rewards decrease, the most expensive mining operations will shut down, keeping the cheaper ones profitable. An equilibrium will be found.
The last point is a problem as it makes the network more centralized, potentially allowing for 51% attacks.
We know that the expected return from newly minted bitcoins will reach zero at some point in the future.
We don't know if expected return from tx/fees will ever hit zero.
TBH if it ever got back to the point where I could mine a block every couple weeks with a GPU, and I had access to a GPU, power source and internet connect I'd probably start mining again.
IMO Bitcoin exists as an interesting and historical concept in too many people's minds for mining to ever stop. The real worry would be that mining drops off to the point where 51% attacks are viable on the bitcoin mainnet.
We'd potentially see that if many large miners either started renting out their services to the highest bidder or sold all their miners. Once we see more hashpower for rent or purchase than goes into honest mining we have the potential for a 51% attack.