How do low interest rates negatively impact bank earnings?

Unless someone can get a bank analyst to weigh in, it will be hard to get a definitive answer on this one.

The first thing to keep in mind is that bank regulations and hedging practices are radically different now than in the pre-1994 era. The Savings and Loan industry was compromised by the Volcker shock (early 1980s), and many people base their views on that episode. However, regulatory practices were overhauled to prevent a repeat.

In any developed country, bank regulators monitor the interest rate risks of banks, as do the banks themselves. Expecting interest rates to rise has been a consensus view for decades, and bankers were not outside that consensus. If the interest rate risk is (largely) hedged, then yes, bank earnings are largely insulated from interest rate movements.

Some people look at yield curve slopes, and claim that they are important for bank earnings. However, they are often working with pre-1994 models. If interest rate risks are roughly hedged, then the effect of the slope is minor.

The general absence of banks facing difficulties during the few interest rate rises are evidence that the regulators are doing what they say they are doing.

One can argue that deposits paying 0% are no longer cheap sources of funding, but this would likely only be material if interest rates were very negative. Banks generate fees off those deposit accounts, which offsets this drag.

I think the main reason for concern is that bank profitability is impacted if they cannot pass along negative interest rates to depositors. If you look at the example of Europe, banks have not been able to pay negative interest rates to consumers despite ECB policy rate being negative. Indeed, the ECB has been forced to implement cheap loans to banks (TLTROs) to help boost bank profitability. Given the huge sums of money involved this effect can be material even for modestly negative interest rates. For example 50bp on the whole deposit base of a bank.