Hey Nick,
It seems like some of script conflict with Easyblog, I already help you turn on "Render EasyBlog's Own jQuery library" setting from Easyblog backend, you should able to see it will refresh the page when you choose 'draft' filter (screenshot :
https://www.screencast.com/t/RL9y0j6dXwjp ).
If after you click on that draft filter, it still show nothing, perhaps you can provide us with your current login user credentials so we can better have a check? because i tested login as nickbb user account, it did show these following draft. (screenshot :
http://take.ms/TW70F )