If you want my knee-jerk opinion, I think this is not a good idea. First, comments are transient, highly likely to be removed at some point, and not at all a space for extended discussions. As How do comments work? notes,
Comments are intentionally short
If the issue can't be resolved in three to four comments - my rule of thumb - it should probably be taken elsewhere, i.e. chat. You should, after a certain amount of back and forth, see a message allowing you to instantly create a chat room with the comments between you and the other user. When this happens, I say Carpe Diem! Take the opportunity. (Note that moderators may also move long comment threads to a dedicated chat room for the post.) Chat has a much better interface for understanding who's talking to who, especially when there are a lot of people talking effectively at once, and it makes the post a lot cleaner on the main site.
You can always take the discussion informally to our chat room, The Factory Floor. I promise we don't bite.
As for whether you should continue the exchange at all . . . I feel it was still sort of productive. There's been no response to your last comments from the other user, which could signal that they wish to end the discussion. If that's true, you should respect their decision to not prolong this anymore - in my opinion. Even though it's clear that you mean well, I think, they may interpret three or four or five or more comments in a row as harassment, however they're phrased. And that's not great.
Bottom line: This is not, by far, the most egregious case I've seen, but for something like this - more than a quick request for clarification - I would have suggested moving it to chat a couple comments earlier. I would also advise waiting before attempting to respond to the other user, so you know if they even want to continue the exchange at all. If they don't, it's not productive.