Hi, hope you don't mind me adding here, but I have the same issue.
There are various tweet buttons (homepage) but when I tweet, there is no "view summary" and no card. It was working until yesterday when I turned off the card output (via Yoast plugin), but since I reenabled and adjusted the text output with the Tweet, it stopped working.
This is the site/page: http://saveafricanhistory.handsupstaging.com/
Been testing it here: https://twitter.com/reflexlabtest