I used to drive a 1990 Accord EX Coupe with an automatic, had the same engine and transmission as the 1993 models. There are two common failures for those cars.
1) The transmission computer (TCU) tends to blow out a capacitor on the circuit board and malfunction, this happens with age. You can buy a rebuilt TCU for $175, it is easy to replace and is under the passenger floorboard carpet. It only has 4 10mm bolts, very easy to remove. If the ECU is malfunctioning you will get a blinking S and/or D light on the dash. I had to replace my TCU at about 110k miles. When my TCU died, the transmission wouldn't lockup the torque converter and sometimes would only shift between 2nd and 4th. The S light on my dash would blink after about 3 minutes of driving the car, indicating that there was a problem.
2) The vehicle speed sensor also has a tendency to fail on these cars. Again it is cheap and easy to replace if it does go bad. When the VSS went out on my 1990 accord the speedometer would randomly not work and the torque converter would unlock at random intervals while I was driving. Sometimes the car would also throw a check engine light, but not always. Replacing the VSS cured the problem immediately.