How can I stop getting File History Backup Error 0x80070003?

I would suggest you to run check disk and see if that help, the following are the steps to run check disk
1.Open Computer by clicking the Start button , and then clicking Computer.
2.Right-click the drive that you want to check, and then click Properties.
3.Click the Tools tab, and then, under Error-checking, click Check now.
If you're prompted for an administrator password or confirmation, type the password or provide confirmation.
To automatically repair problems with files and folders that the scan detects, select Automatically fix file system errors.
Otherwise, the disk check will report problems but not fix them.
To perform a thorough check, select Scan for and attempt recovery of bad sectors.
This scan attempts to find and repair physical errors on the drive itself, and it can take much longer to complete.
To check for both file errors and physical errors, select both Automatically fix file system errors and Scan for and attempt recovery of bad sectors.
4.Click Start.


If the above steps fail, I would suggest you to try the following steps.
1. Click Start, and then Run.
2. In Open, type cmd, and then press ENTER.
3. Use one of the following procedures:
o To run Chkdsk in read-only mode, at the command prompt, type chkdsk, and then press ENTER.
o To repair errors without scanning the volume for bad sectors, at the command prompt, type chkdsk volume:/f, and then press ENTER.
o To repair errors, locate bad sectors, and recover readable information, at the command prompt, type chkdsk volume:/r, and then press ENTER
once you complete the above steps, I would suggest you to disable all security software and then try back up again.
I would also suggest you to make sure that you have full permission given to the drive for which you want to back up the files.
1. Click Start, click My Computer, and then locate the file or folder where you want to set special permissions.
2. Right-click the file or folder, click Properties, and then click the Security tab.
3. Click Advanced, and then use one of the following steps:
A. To set special permissions for an additional group or user, click Add, and then in Name box, type the name of the user or group, and then click OK.
B. To view or change special permissions for an existing group or user, click the name of the group or user, and then click Edit.
C. To remove an existing group or user and the special permissions, click the name of the group or user, and then click Remove. If the Remove button is unavailable, click to clear the Inherit from parent the permission entries that apply to child objects. Include these with entries explicitly defined here check box, click Remove, and then skip steps 4 and 5.
4. In the Permissions box, click to select or click to clear the appropriate Allow or Deny check box.
5. In the Apply onto box, click the folders or subfolders where you want these permissions applied.
6. To configure security so that the subfolders and files do not inherit these permissions, click to clear the Apply these permissions to objects and/or containers within this container only check box.
7. Click OK two times, and then click OK in the Advanced Security Settings for Folder Name box, where Folder Name is the folder name.

Bobold,
Run your disk check this way............................

Right click at Start button > select Command Prompt (Admin) > at the flashing prompt, copy & paste this..................
chkdsk /f/r

> Enter.

The black and white screen will tell you that (paraphrasing) it cannot be done now, but do you want to do that on restart.
Type Y as in "yes" > enter.
Exit command prompt.
Restart computer.
Disk check will commence at restart.
When finishes, it will give you a report and then it will take you back to your desktop.