With reports of problems with both the iOS update to 1.3 and with the corresponding update to the Android version which I also experienced, I checked my iPad. The app still works on my old iPad 2, still downloads from DropBox even though it is running the Dec 2015 version 1.2.1 and despite not having done the update to 1.3 for the DropBox API rev. I'm wondering whether there is any merit in updating to 1.3 if it means risking breaking something.
What does seem to be different from before is that repeated RootsMagic 7.5 Save to Dropbox results in serialized files on Dropbox instead of one file whose name does not change and whose change in timestamp triggers a notice in the iPad app. Now I get no no notice and I have to manually select and download the new file and delete the old from my device.
I don't know if the multiple versions of the database file on Dropbox is a consequence of a change in the API or a change in the way RM 7.5 uses the API. I haven't made much use of it so I cannot identify when it began.