PearsonArtPhoto's answer, while not wrong, isn't entirely accurate.
It is absolutely true that diamond-wielding moderators and Stack Exchange employees can delete any comment at any time. Moderators and employees can delete specific comments, all comments, or delete all comments but undelete specific comments (thus making it appear like all comments but a specific few were deleted, but the mechanics are different).
Comments can also be deleted if they meet certain criteria involved in flagging. For example, if a comment is flagged as "rude or offensive" by a sufficient number of users it is deleted, but comments that contain certain key words and are flagged as "rude or offensive" are deleted immediately by the system even when flagged by only a single user. There's a small list of words that trigger this behavior; I'm not sure if it has actually been made public (probably not), but they aren't words that you would be likely to use in a constructive comment.
Comment flags that do not meet the criteria for auto-deletion of the comment show up to the site moderators for evaluation and action. Diamond moderators can see deleted comments, so if you feel that a comment was deleted in error, you can flag the post for moderator attention and request review; however, it's likely that such a flag would be declined because in the Stack Exchange system, comments are second- or third-class citizens and are generally considered as ephemeral, subject to deletion at any time for almost any reason. Do not get to attached to them, especially on the main sites (Metas may be a bit more forgiving).
It has been suggested, and largely argued against, to implement notifications for deleted comments; also here and here (among others).