Is there anything we can do to stop these attacks when no one will stay mining? or....
Miners will still be there. Not for the Block Rewards, but for the Fees. Even if there was no monetary incentive for Miners, Bitcoin will more than likely continue to exist. There are enough enthusiasts to have at least a couple hundred Miners using their little power 24 out of 7 to sustain the Bitcoin economy.
No more Block Reward means nothing bad in my opinion.