I don't have FMS 12 installed on anything. I download your sample database to my ipad 3 and run it in FMGo 13 and FMGo 14 without issue. It displayed dropbox login screen close the login screen then it displayed a flyer. Went the next record which had a photo of a jeep on google drive. I went back and forth between the two records 3 or 4 times. FMGo 13 has a memory leak issue, that maybe the cause of your problem. You have to close FMGo by double tapping the home button then swiping up on FMGo to close it. If you still have an issue then I would suggest remove FMGo and reinstalling it again.
PS FMGo 13 may be removed from the Apple store soon, FMI extended the removal of FMGo 13 but it is not compatible with ios9 that is going to be release in a few weeks so FMI will not have a choice but to remove. Make sure you install FMGo13 on all your devices then you can always go back to reinstall if needed, even after it has been remove from the App Store.
I know a bit late but this issue has been resolved by itself - meaning that the issue had to have been with google drive updates and not with FM itself
Google Drive had issues with many of their servers I guess but eventually all problems went away