With its use, the scarcity of numbers remain, that is, finding a clash that would allow to forge a transaction stays infeasible, and mining stays hard.
BTW while mining is so important with Bitcoin and Etherium, it's not a necessary part of a cryptocurrency. Mining is an incentive to keep doing blockchain validation. Some currencies exist without it (e.g. NXT).
Post-quantum cryptograph research is a very active area right now. If these researchers do not find a practical signature algorithm, PKI as we know it will change very significantly.
Ironically, blockchains might elevate in importance as a result, since the evolving blockchain is a useful construct for quantum resistance. It has cryptographic agility built in.