If you mean that you are having a discussion with someone, and that person wants to stop talking (and maybe leaving the place where the discussion is happening/maybe leave you by yourself), then, to be respectful I would say "Please don't leave this/our discussion or Please don't stop this/our discussion or Please, let's continue this/our discussion."

"Let's continue this discussion. Let's not run away from it." This may well be what the modern diplomatic native speaker would say.

I think what you mean is "don't avoid the/this discussion" or "don't try to get out of discussing this." There are likely many ways to say what you mean.

Hi, To give you a full answer I need a bit more context of the situation. However, you could say 'don't try and escape from the discussion'