Well, not sure what specifically you are concerned about losing, so not able to guide you there. I can tell you that I have backed up both my iPhone 4 and my iPhone 5s to iCloud, then erased and restored them (for testing purposes), and they have restored to the condition they were in prior to the erase. It takes awhile for the apps to reload, but other than that I have not noticed anything missing.
If you do decide to go the restore route, I would recommend that you first set up the phone as a new device (not from the backup), then sign into iTunes and see if you are able to get things working the way you would expect them to. If that works, then erase again and then restore from the backup. After everything is done restoring, try the sign in again, and see if the problem comes back.
If it does, then you know that you have some corruption in your data or apps, and you may have to set it up as a new phone and manually restore it bit by bit (checking as you go so if there is a specific app or other item you are putting back on the device that is the culprit).
This can be a bit time-consuming, but if there is some specific app or media that is causing the issue, this route would allow you to isolate it.
Best of luck!
GB