A not entirely useful answer
Well, it probably does no good for me to say I can see it, since I have general delete authority over any post.
But, presently, I see four buttons in the quick edit, and also have the delete option if I Go Advanced.
As you're editing a post, I presume your attempt is within a forty-eight hour window?
And I should note that I cannot definitively say I have encountered the last of the performance differences between the former version of this site and the updated software. If I can get a little more information from you, I can check in with the administration to see if we've made any changes to post edit permissions that I'm unaware of, or simply forgotten about.
Meanwhile, is there a particular post you wanted struck? You can note it here, or advise me via PM.