I find it helps to slow down to give myself space to think properly, instead of automatically assuming my brain will take care of it.
I have got really bad at being caught on the hop too. I was always good at winging it, and never prepared or wrote things down. Now, even if I get the words out, I don't always manage to say what I mean and come out with a load of woolly gibberish.
I have to write a list if I go to the doctor or any sort of meeting. In that sort of situation (and they are usually time-limited) it seems to signal to the other person that there is actually something to say and they will wait for it. I learned that when I saw the urogynacologist consultant for a rectocele repair, and realised that I was not able to project what I was intending to say properly, and as he was a fast thinker and not particularly people orientated, I needed to stand up for myself. I do that as much as I can now. (It was worth it too - he originally prescribed my vagifem)