I have had a few people say that they could not leave comments on my blog recently. I had this same thing happen to me when I was trying to comment on blogs a few months ago. Here I would check if you are experiencing problems posting . . . this is straight from the Blogger Help Forum
1) If your users are Firefox/IE users they need to make sure they have 3rd Party Cookies installed.
2) If you have word verification turned on. People with popup blockers will probably have problems with this. It's advised to turn this off as Blogger now has Spam Filtering
3) If you make your comments Full Screen instead of Embedded/Popup then more people will be able to comment on your blog.
4) Check your Comments Tab to see if they are getting Moderated. Pay particular attention to the Spam section.
5) One thing to try, but backup your blog template first, is to try resetting all your defaults. see screenshot. You do this from the Design, Edit HTML screen.
6) If they are having trouble logging in get them to UNTICK the remember me checkbox
7) There is a KNOWN ISSUE affect IE8/9 users currently