Why won't my iPhone back up to iCloud?

It says iCloud backup failed. There was a problem enabling iCloud backup.

Try these:

Reset Network Settings: Settings > General > Reset > Reset Network Settings

Delete all unnecessary backups existing not really needed: Settings > iCloud > Storage > Manage Storage. (This works magically on many users)

Upgrade to latest iOS version if available.

Hold the Home + Wake buttons together till the device reboots and the apple logo appears, then attempt to backup with iCloud.

Maybe your iCloud storage is used up, delete some backups you don't need and try again.