Sluggish Response

After reconnecting my battery (had been disconnected for 2 days) my car was very sluggish for the next three short trips (2 miles, 2 miles, 10 miles). On my fourth trip it seemed to be cured after about 5 miles. Does it have anything to do with resetting the ECU?

Depending on the year, make, model, engine size, ECU design, etc., the adaptive fuel trim tables may be lost when the power is disconnected from the computer. It does take several driving cycles for the computer to relearn the old appropriate values to make the engine run correctly.

So if I take my car in for some type of service in which the battery is disconnected for a day, I would endure this same type of problem or would the servicer program in some defaults?

On most cars, the ecm goes into a “learning mode” after the battery is disconnected for more than a few moments. During the learning period, rough idling and sluggish response is typical. It sounds like your mystery vehicle reacted as expected and is now back to normal–as expected.