In most instances, a business bleeding red ink has a big problem and could ultimately go under. Not so for the Fed. In fact, losing money isn't a problem for the central bank at all. But it is a big problem for the US government.
According to the Federal Reserve's quarterly report for Q2, the central bank reported a loss of $57.3 billion through the first half of the year. The Fed is on pace to lose over $100 billion in 2023.
Rising interest rates are a big problem for the Fed, as they are for other banks. The central bank earns interest income on the bonds it holds on its balance sheet. But the Fed also pays out interest to other financial institutions that park money there. The bonds it bought during multiple rounds of quantitative easing (QE) and still holds on its balance sheet were relatively low-yielding. But with rates much higher today, it is paying out interest at a much higher rate.