Ok, it sounds like a database migration issue. The best solution would have been to leave the URLs alone. Connections does not really care about the origin domain, only the relative path to the uploads folder. The URL will auto-adjust to new domains. My guess is because this data is saved in the entry option as a serialized array, that data was corrupted when the URL was changed from the old to the new. This would explain why changing the URL back worked and why you would not see the URL in the CSV export.
For the images for the entries which that did not fix, my guess is the serialized array is still corrupted, even with the change back to the old URL as the data for the image is saved exactly the same. The entry type does not matter. My suggestion is to look at the old db and compare that with the new on the entries which do not have an image and should to see what the difference is. You probably will be able to craft a query to fix the corrupted serialized array and restore those images too.
The only other option would be to reupload them.
Hope that helps. Let me know.
ps. I’ve found the best way to migrate a site is using BackupBuddy or Duplicator. And if moving just the Connections data, to do that manually by copying the connections-images folder to the new site and then exporting the as a SQL file the Connections tables and them importing the Connections tables on the new site. The only real change you would have to do is make sure the table prefixes WordPress uses match after the import.