"No sabía cómo responder (o "No sabía qué decir.") In most situations this would be what you were trying to say, because you are going back to that ongoing state of being during the time when you didn't know how to respond.
Originally Posted by Yacamaca
If, however, you're talking about some fixed period in the past, then you could maybe use supe. For example,
They asked me that question 100 times when I was younger, but I never knew how to respond.
Me hicieron esa pregunta 100 veces cuando era
más* chico, pero nunca supe cómo responder.
But if you're going back to some specific moment at which you didn't know how to respond, then you are sort of revisiting your state of being during that time, so that it becomes an ongoing state. Because of this, the imperfect is the natural choice. Since this is the most frequent case, way more often than not you'll hear ...no sabía cómo responder.
There are a lot of WR members who know more about this than I do. Maybe one or more will make this more clear for both of us.
*Me informaron que no se usa "más chico" de esta manera.