I recently made a comment in response to another comment on the answer to this question. I just noticed that both had vanished and was wondering why. Is this perhaps a bug or is there another explanation? It's not that I particularly care about a disappeared comment, but I've never seen this behavior before. (If there was a way to put a question mark after a tag, I'd have done so.)
In the words of the official guidance, “comments are temporary "Post-It" notes left on a question or answer”.
In practice, a lot of comments stay around indefinitely. However, when a comment has outlived its usefulness, it is ideally deleted. You can vote to delete an obsolete comment by flagging it as “obsolete”. To flag a comment, click on the flag-shaped icon that appears at the left of the comment when hovering over it. A popup will appear and you will be able to select a reason to delete the comment. Besides obsolescence, reasons to flag a comment include rudeness and irrelevance to the post that they are on.
Comments are automatically removed if they receive sufficient flags in a certain time period. This hardly happens on this site; comment flags are also seen by moderators who will delete the comment if they agree with the flag. Comments can also be erased by their author.
In this case, your comment was intended to another user, and was not generally useful to other users. After this user had read your comment, it no longer served as a useful purpose. Your comment was flagged, and removed by a moderator.