Does this happen? Just as with being rejected, of course it does. We don't know everything and the right answer doesn't always pop into our heads at just the right moment. However, our not knowing an answer gives us an opportunity to continue the conversation later. We can reply, "That's a good question. Let me think about that/look into that and get back to you." (Actually, my teachers in school would say, "That's a good question. Research the answer and get back to the class on that.")
No doubt some people would remind me of Luke 21:12-15 wherein Jesus promises to give us the words to defend ourselves. In that passage he is speaking about a time of intense persecution where we are called upon to uphold the gospel in defense of our life. That is not describing the ordinary situation where we are speaking to a neighbor or friend. It is describing an extraordinary situation where our life is on the line. Jesus will supply all the words we need at that time.
For reflection: Has my light been dimmed by fear? If I am afraid I don't know the answers, am I studying the Bible on a regular basis?
Let us pray. Jesus, I want my light to shine. I want my life to reflect your glory. I want people to know that my life is different because of you. I give you my fear of rejection and my fear of not knowing enough. Is there someone to whom I can speak about you today? I'm volunteering. Send me.