• If you have a DATE or a TIME field, it automatically updates.
• If you use CreateDate fields, it remains fixed at the date the document was created, which does not seem to be what you want

Using Date Fields in Microsoft Word

• You can lock or unlink such a field so that it will not update.There are keyboard shortcuts available to do that.

Function Keys and Keyboard Shortcuts that Manipulate Fields

The macros that I gave insert text, not fields. That will not automatically update. If you want, download the template with the macros, open it and assign keyboard shortcuts or QAT icons to them (saving those macro triggers in the template, not in the normal template). Then store the template in your Word Startup Folder. From then on the keyboard shortcuts / QAT modifications and macros will be available in all of your documents.

Modifying the Quick Access Toolbar (QAT) in Microsoft Word