I commented on Session cookies seem to get lost and then, later while on another site, I was notified about Aaron Bertrand's comment reply. After responding several minutes later and, because I believed my earlier comment didn't apply to this question, I deleted it. However, I then noticed that Aaron's comment was no longer in this site's list of comment responses, nor in my global inbox. Interestingly, the latest notice there is to a comment of a question which was deleted by the OP about 3 days ago.
This is, as far as I know, unexpected behavior. The only possible cause I can think of is, although it was at least a few minutes after Aaron's reply, that I had deleted my earlier comment. I've personally seen this sort of behavior happen before, but only when I've deleted a comment before the reply was posted.
To help avoid duplicates, I initially searched the site, but the only somewhat related posts I could find were Do @replies to deleted comments work, too?, If I leave a comment, then delete it, does a person still get notified?, and Deleted comments are persisting in the global inbox.
Update: This behavior is implied in the duplicate question, where it asks
Does User A get a notification for the reply of moderator C if the target comment is removed? Does it matter if the moderator removes the comment before or after writing their own comment reply?
with the answer there stating
No, notifications for deleted comments only persist if it is to the author of a deleted post.
Note that, as I've found, this issue of removing the notification of a comment, where the source comment(s) have been deleted, generally applies to not only with diamond moderators deleting that comment, but also to when the owner does so themselves. Nonetheless, there are several exceptions with diamond moderator's comments in a deleted post, as explained in the later linked answer.