Hi,
I have been having this issue. It only happened when the new IOS was deployed. I manage 10 iPads at a public library and I learned a lot, though I am not really certain of any of this. I will share a little of what worked for me.
1. My iPads have updated to the new IOS.
2. When that happened, the backup of my bookmarks, etc. will not restore.
3. I tried to set the IOS to never update, and Configurator would not restore.
4. All those white screened iPads probably need to be re-set-up as their own user. like publiclibrary001@icloud.com, publiclibrary002@icloud.com, etc. They need their own password, etc. I say "probably" because I keep trying to share the same username even though I know I'll never be able to install VPP apps for them like that and plan to re-assign apple IDs to each.
5. Today I get Error code 4 on my Configurator and the backup will not work, so my bookmarks are "flushed" and I don't know how I'll restore them. I may submit and create apple IDs for each one today.
6. It was possible at one point to go through the setup screens on one, decline to set up "Find my iPhone" and then make a backup of it. Restore the new backup to all iPads, then re-set them up as their own machines, save a backup for each individual one, then setup Find my iPhone. THEN, re-save a new backup of each individual one. That worked for me really great until yesterday when I get this Error Code 4.
7. I really liked having them all share an apple ID because when I log into iCloud.com, I can see all iPads on one map.
I may check in with my result since it seems there is no reall official support for Error Code 4 yet.
-Ilan