Strange!! may I know what have you copied , only text, the object(frame containing text).
Have you just copied them or they have retained their linking with the original text. And when you say making corrections is that you are making corrections to the original word document or the first placed instance of it.
The copying is straightforward highlight text, copy (clipboard), paste in template. The destinations at that point still are good.
The corrections at that point are all made to the text as placed in the template, which is now the working doc.
Originally I thought that the copy/paste was the issue, but if the destinations are still there in the pasted text, what would subsequently make them disappear? Is there some sort of linkage to the original doc that is taking place, so that once the new doc or the original changes location/address the links are broken and the destinations lost?
It depends on what type of Hyperlink you have created. Each hyperlink has a destination and some are shared destinations. When you place a word document having hyperlinks in them to InDesign document these hyperlinks come to the InDesign document and point to hyperlink destinations which are also created with the place. (you can see hyperlink destinations in Hyperlink panel flyout menu.)
Now when you copy the hyperlink from InDesign document to another document the hyperlink text is copied but this Hyperlink destination remains in the first document and as soon as that document is no longer accessible (you maybe deleted it or moved it to a new location) the hyperlinks in the second document don't have a destination to point to.
What you can do to solve the issue?
Either somehow use the same document as the template.
Or make sure that the hyperlinks are not shared destination hyperlinks, to do so open the hyperlink(double click on the name of hyperlink in the Hyperlinks panel) and there is a check box below the URL field "Shared Destination" un-check it and then copy the hyperlinks.
There are 2 ways of creating a Hypelrink
1. Select some text and in the hyperlinks panel type in the URL in the URL edit box.
2. Select some text and in the Hyperlinks panel click on Create New Hyperlink button at the bottom of the panel, that opens up the New Hyperlink dialog, in the dialog there's an option "Shared Hyperlink Destination", uncheck it and you wont create a shared hyperlink.
With the first you always create a Shared hyperlink destination.