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I don't have an answer. My experience lies with VBA in Excel not Word.

As an experiment, I created a third UserForm using the same CommandButton code as the other two userforms. This new form
disappeared as well after clicking the button.

I reviewed all of the code in all Userforms and Modules in the example download file provided in the resource link you posted.
I cannot find any other references to closing or hiding the userform in the code.

I am at a loss to explain.