No. Comments should not expire at some predetermined time. Good comments may point out faults with the answer - particularly on less subjective sites. If these faults are not addressed - either by clarifying or correcting the post body - that doesn't make the comments less valid. If only the OP can clarify, we can not fully judge the post - whether a question or answer. These comments should be a signal to others that the post may not deserve an upvote because they are unclear or imprecise or completely wrong. Removing them is a disservice to the people who come after to judge the post.
A user who is inexperienced may take a post with some upvotes and no comments as a good answer. If that post had originally had a comment questioning the correctness - by asking for supporting information or documentation - this would tell the inexperienced user that they may want to find a better solution to this problem.
If a comment is a +1 comment or a joke comment or argumentative, it should be flagged and the moderators can either remove it or move the chain of comments to chat.
In relation to your specific answer:
The main gist of the comment I left you is that your answer fails to explain itself.
Why would you do this? Answers need to support themselves and explain why they are good solutions. If you've been in this situation before, feel free to share your experience. If you have not, explain why you think this is appropriate. You've mentioned some of this explanation in your comments... please don't leave it there - add it and any other detail to your answer.
The initial revision of the comment actually did not include the final sentence as I hadn't seen the comments you had posted. If you think those comments are tangential to the question/your solution, you don't have to include them but that does not mean that your answer should not include support at all.
From practically the beginning of this site - the very long duration of less than four months ago - we have debated what we expect answers here to contain. One of the things that we seem pretty strongly to feel is that we need answers to back themselves up.
If an answer calls out directly relevant personal experience, or reference materials, those are signs that the answer likely deserves an upvote. If the answer instead provides what seems like sensible advice, backed with an explanation of why that advice seems applicable to the situation, fully answers the question, but doesn't explicitly state what parallel experiences happened to the author that they are basing their advice on, that's fine, too.
If instead, an answer is brief, low quality, and doesn't seem to stand on its own, it is appropriate to downvote and add a comment saying "answers on this site should be backed up with either a reference, or experiences that happened to you personally", with a link to (our hopefully updated) help center.