The macro is hitting the body of the document and may be missing floating text boxes and header/footers for instance. Also, if your fields are locked or protected by 'restricted editing' then it is possible this is causing your issue.
You may need to post a sample document so we can see what you have going on in your document. Have you changed Word versions since you last saw the macro working? Are you sure the macro is actually running? If you add a msgBox line in the code you can get feedback to know the code is being executed.
Code:
Sub UpdateAllFields()
MsgBox "Running the UpdateAllFields macro"
ActiveDocument.Fields.Update
End Sub