The problem of the Normal template not saving must be dealt with separately. You should troubleshoot for poorly designed add-ins; see
http://support.microsoft.com/kb/921541/en-us/.
In the meantime, you can work around the issue by opening Normal as a document and creating the Quick Part directly in the template.
To open Normal.dotm as a template, do the following: From within Word, hold the Alt key as you press F11; in the Visual Basic Editor, press Ctrl+G to activate the Immediate window. Type
NormalTemplate.OpenAsDocument
and press Enter. Normal opens in a separate window (and you should now close the Visual Basic Editor). Make the desired changes, save and close the file.