From How do comments work?
Comments are temporary "Post-It" notes left on a question or answer. You should not expect them to be around forever. Once a clarification has been made, an edit added to the post to include new information, or the issue in the comment is otherwise resolved, it is subject to deletion. In reality, many obsolete or chatty comments remain untouched due to the high volume of comments posted, but this does not mean that they can't or shouldn't be deleted in the future.
Yes, we know that it is off-putting to people to delete discussion in the comments. That doesn't mean that it's the wrong thing to do, especially on a site where a good portion of the community isn't fluent in English and really needs us to vote so they can tell what is credible.
You will notice that it tends to be comments directly under the question that get moderated most heavily, because that's where people tend to put things that seem like answers. Comments under the question also push answers, which are far more valuable, down the page where they are less likely to be read and voted on.
Often comment discussions cause authors to disengage from their question, because what learner wouldn't prefer a one-on-one discussion to an answer written to be useful to more than just one person? Once they have their answer they move on to other things, and ELL still doesn't have a proper answer for future visitors that will show up in a search engine.
Comments under an answer ideally should be addressed by editing the answer to either incorporate the information or address the concerns (as Nathan already mentioned), but that doesn't always happen. Because the comments under an answer can add valuable context or additional information and they do less harm than comments directly under the question, they are often left alone. That should NOT be interpreted as "go ahead and chat in comments as long as you do it under an answer" though.
I haven't checked with the rest of the moderator team, but if anyone would like a chat room set up for discussion on an answer, I am happy to oblige - just leave a flag for a moderator on one of the comments or ping me (type @ColleenV and your message) in ELL's main chat room Language Overflow and let me know.