In an ideal Q&A site comments shouldn't exist at all. From the about:
Ask questions, get answers, no distractions
Comments exist with the only purpose of refining the content of a post and not for extended discussions.
It's consider good practice to remove comments whenever appropriate, for instance when the OP clarifies their question and the comment is now useless. You said (in the comments, consider moving this to the question):
I've experienced, several times, where a user and I had a couple exchanges, and he ends up deleting his comment some 20 days in the future, which makes it look like I'm talking to myself.
People are aware that comments can be easily deleted: nobody will think you are crazy, just that there's some missing comment you are replying to.
The other person decided to remove his comments since he though they weren't worth to stay there. If you notice something like this, it's a wonderful occasion for deleting your comments as well and keeping the post as clean as possible.
Bottom line, the focus should be on the content of a post, not on the comments. Locking the comments after X days, as you suggest, would directly go against the fundamental principles of StackOverflow.