How can I stop my iPhone displaying "iCloud Backup requires that you verify your password" repeatedly? Due to what turned out to be a (I assume unrelated) sim card problem, I recently wiped my iPhone 4, and then reinstalled from a backup.

Since then, multiple times per day, my iPhone displays a "iCloud Backup requires that you verify your password" message, and then prompts for my iCloud password. If the correct password is entered, the prompt is dismissed, only to return after a few hours (I've not noticed any specific triggering action I'm performing).

How can I stop this prompt from appearing repeatedly?

Presumably disabling the iCloud backup, as suggested at https://discussions.apple.com/thread/3406796 would do the trick, but I do still want the backup enabled.
I personally had this same message. I turned off iCloud backups, then turned it back on. Settings > iCloud > Backup. While it did ask for my password the first time, it has not asked since.

If that doesn't work, I suggest to again, turn off iCloud backup, delete the backup, then turn it back on.


Settings > iCloud > Backup, turn off.
Settings > iCloud > Storage >
Manage Storage, locate the backup, tap edit in the top corner, and
delete.
Settings > iCloud > Backup, turn on.