Ask HN: How to Listen to Questions?

I think you all have been in this situation: you are going to present your work to a large audience. You're nervous, perhaps the demo you prepared so carefully didn't play as good as you wanted. You keep going, the audience seems interested, you're happy. You finally reach the slide you're proud about.

And then a question comes. And then another question. And another. They seem critic.

And you just stop listening to the questions. You wait for them to finish, and then reply with some random sentences vaguely related with the topic of the question (if you are lucky).

That is: you just stopped listening.

The situation above is just an example. The same can happen in a chatroom, or on an email thread while you defend your design doc. The point is: it looks like your brain just does not want to listen to the question. You repeat it in your mind, and still you don't get the point.

How do you handle these situations? Do you recommend some specific approaches?