This may happen if the password for the network backup volume has changed since Time Machine was originally configured. Log in with the user account that was used for the initial Time Machine configuration, then reconfigure Time Machine in System Preferences by selecting the backup volume again.
Alternatively, you can use Keychain Access while logged in with the affected user account:
- Open Keychain Access (in /Applications/Utilities).
- If the Keychains list is not shown in the upper-left corner of the window choose Show Keychains from the View menu or press Command-K.
- Select the "System" keychain in the keychains list.
- Find the Keychain entry in the System Keychain whose name matches the computer or Time Capsule you are backing up to and whose Kind is "Network Password".
For example: If your Time Capsule is named foo the correct entry may appear with a name of "Foo.local" or "Foo._afpovertcp._tcp.local".
- Double-click the keychain entry to open the inspector.
- Click the "Show password" checkbox and enter an administrator name and password when prompted to authenticate.
- If the displayed keychain password is not correct then enter the correct password and click "Save Changes".
- Repeat this process for all keychain entries of this type for the computer or Time Capsule you are backing up to.
- Quit Keychain Access.
- Choose Back Up Now from the Time Machine menu extra, or choose Back Up Now from the contextual menu that appears when you Control-click (or "right-click") the Time Machine icon in the Dock.