The message 'The last backup could not be completed.' is nearly always displayed if you start an iCloud backup the first time.
It's unrewarding like many other error messages shown on any devices.
I get this message every time I delete the last iCloud backup for my iPad or iPhone going to Settings - iCloud - Storage + Backup - Manage Storage - (device name) - Backup options: Delete Backup
It never occurred on any later incremental backup regardless of whether it was started manually or automatically.
At the time you cannot find any support document on Apple's support website explicitly mentioning this error message.
Apple iCloud: Troubleshooting creating backups
http://support.apple.com/kb/TS3992
For the protection of our customers, Apple does not disclose, discuss, or confirm security issues until a full investigation has occurred and any necessary patches or releases are available.
So it is not fully investigated and there are many potential reasons for failing backups.
Best practice ...
Do not believe all these statements in the forums.
They are all not really verified and based on special prerequisites and thereforee are not necessarily valid.
I start a manual backup every month since the release of iOS 5 after deleting the backup via Settings - iCloud - Storage + Backup - Manage Storage - (device name) - Backup options: Delete Backup. The following procedure works since more than one year.
Reboot the device and start a backup manually while the device is connected to the power supply.
If the backup fails repeat it.
Don't worry. Retaking a backup will only last some minutes unless there is already stored data of former attempts.
Note
When you back up the device shows an estimated time to finish.
You should know that these minutes are measured in DAMs (Dynamical Apple Minutes).
An Apple Minute may last an old fashioned minute or two or just 30 seconds.