"Copy Links To" option in the Links panel does not flag as a change in the document.
Therefore, InDesign does not prompt to save the change and the document continues to link to the previous location if closed. I was able to reproduce this problem on MacOS High Sierra and Windows 10 with both InDesign CC 2017 and 2018.
Ya, I also just noticed that "Save As" can be used as a workaround, to ensure that the new link location gets saved. Funny though, I never noticed this bug until today. I must have been lucky up to now, making other changes to the file which saved the link locations as well.
Stan, until Adobe chooses to fix this bug, another workaround is to use the "Copy Links To" option in the Links panel and then return to the document and make a minor change, such as nudging an object on your page. This will then detect a change to the document and will allow you to save the updated locations of your links.
I just had the exact same thing happen to me. I saved an InDesign file to a new location. Then I did "copy links to" the new location. It showed the proper NEW address for each link. But when I closed the file and re-opened it, all the links were for the OLD location. My only solution was to "relink" each link to the new location.