Low rates will certainly compress margins for banks, especially regional ones. This was evident coming out of the credit crisis when interest rates started rising, the rate of increase on deposit rates was much slower, indicative of banks normalizing their margins.
However, I don't see that as a big problem outside of norms. They "simply" need to stay healthy and survive the period and be positioned for growth/big earnings later, possibly with less competition on the back-end. Every business/industry goes through cycles, and this should be their tough period. Where it gets really complicated is if the regional bank's client/loan concentrations are deeply impacted by the economic fallout of this crisis. Those banks will have a tough time surviving if they don't have the right leadership in place to navigate the challenges in front of them.
***Not a banker.