THE TREMORS running through the banking system keep hinting at an undesirable degree of instability. Your federally insured deposit is perfectly safe, since the federal government stands behind it. But there's a lot more to banking than the federally insured deposits, and a bank's failure can do a lot of damage to its customers. The run on the Ohio savings and loan companies with their state-insured deposits was not an isolated episode. In a letter on this page the president of the American Bankers Association, James G. Cairns Jr., takes issue with our conclusion that it was related to deregulation of the financial institutions. Let's pursue the question a little further.

In 1984, there were 79 bank failures in this country, the highest number since 1933. So far in 1985, there have been 19 failures. Each, no doubt, involved poor judgment by someone and a few may have been caused by fraud. How do you explain this sudden epidemic of poor judgment and fraud? Something in the drinking water? Isn't it more likely to reflect a kind of strain on the banking system that is unprecedented in recent decades? Part of that strain is a delayed effect of the last recession, but following the previous severe recession in 1973-75 the number of bank failures peaked at 16 in 1976. It's not good enough simply to dismiss each successive collapse in this trend as a special and separate case.

Deregulation of interest rates has impelled both banks and the savings and loan companies to raise the rates they pay to depositors. Otherwise, they fear, their customers will pull their deposits out and put them in the money market funds. To get the income to pay those higher rates, the banks and S&Ls have been looking urgently for loans and other investments earning still higher rates. But investments paying high rates tend to be risky. Mr. Cairns observes that the failed S&L in Cincinnati was pursuing high returns "through a type of investment in which it had little expertise." Exactly. But this type of investment -- the repurchase agreement -- is simplicity itself compared with the exotica that now flourish in the financial markets.

Interest rates can't be regulated or controlled. But there's a bargain to be struck between depositors and federal insurers. Depositors who want the highest possible money-market rates are not entitled to insurance. Depositors who want insurance are not entitled to the highest rates -- and insured institutions can properly be required to stay away from certain lucrative but complex and risky types of investments that produce high earnings. If a banker decides that he wants to go for the big money in real estate development or securities underwriting, he has every right to do it. But perhaps he ought to be asked to get out of commercial banking first.