Here’s one possible solution to try. My site is approved and all my twitter summary cards work except one page with an image that consistently gave the “Failed to construct resolution, debugId: …” message. Running the page through the Google Webmaster Structured Data Testing Tool led to the message “The server … is taking too long to respond”. I edited/reduced page content so that that message went away. That resulted in the page with the twitter card tags validated and the image displayed in Twitter.
My guess is that the “Failed to construct resolution,…” may not always be indicative of a problem with the image (in a twitter summary card) per se, but page content containing it taking too long to be processed by the validator/twitter. Worth a try as it worked for me.