Comments are ephemeral, and have some specific guidelines on how they should be used.
Those guidelines are not a hard-and-fast rule for when comments will or won't be deleted, but broadly they are not intended to be a permanent record (see Stack Exchange is not a forum), so once comments have served their purpose they are subject to deletion (by the authors or by moderators).
If a comment specifically falls into one of the "When shouldn't I comment?" categories or runs afoul of our network-wide Be Nice policy it also probably won't last long.
As we're a lower-volume site than say Stack Overflow there's a good chance a moderator will see most comments on the site and exercise some "editorial judgment" if the direction the comments are taking is worrisome.
The usual reason you'll see comments disappear is that a user (or the system) has flagged the comments for moderator attention and one of us decided they can be deleted, but the moderators also use the site on a pretty regular basis, and speaking for myself if I see comments that could stand cleaning up while I'm browsing the site I'll deal with them as I find them.
If you have a specific question about a specific comment that was deleted you can ask about it here on Meta: Provide a link to the question or answer the comment was left on, and a moderator can look at the deleted comment history and see what the comment was and who deleted it.