Sometimes as a moderator I take 'organic' moderator actions, in that I'll close a question on the front page just because I saw it, and not because it was in the moderator queue. I've always considered this a normal part of my job.
Today, I voted to close a question for a few reasons. I checked back in my activity 15 minutes later to see if the author had taken any action, only to find the post was gone from my 'comment' activity section even though I had left a comment. The reason the post was gone is that the OP deleted it.
This presented a problem. Because there were no flags on the post, the moderator queue 'recent activity' did not pick up me closing that question, and because the post was deleted, I couldn't see the question anywhere else.
Luckily, I had remembered the user's name, and did a search for 'new users' with that name -- I found him after a few attempts.
In that time, he deleted his old post and he had posted a new question that was a duplicate of his old question.
As a moderator, I do sometimes take organic moderator actions, and I do check up on my activity to make sure I'm following up in case the user improves their post, or something 'goes bad'. Not being able to see deleted posts in my activity section keeps me from being able to do this, and makes it really tough if a user decides to delete a post to get around an issue, as happened here.
This is not the first time it's happened, only the most recent.
Moderators should be able to see their comments on posts that were deleted in their activity section, and any moderator action should show up on either a) their moderator 'recent activity' page, or b) on their activity page under the right section.