That video clarifies what's happening. You're exporting the PSD as a JPEG, adding it to the catalog. There was a previous JPEG of the same name already in the catalog, so you told Export to overwrite it. But LR doesn't re-read the metadata (including the GPS coordinates) from the file that it just overwrote. The badge in the upper-right corner indicates that the metadata on disk is newer than what's in the catalog:
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Click on the badge and you'll be asked:
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If you select Import Settings From Disk, LR will read in the GPS coordinates that were added by the most recent export. You can select more than one such photo and do Metadata > Read Metadata From File (but be careful to do this only with photos that were just updated by the export).
As you observed, the first time you exported the PSD back into the catalog, LR read in the metadata from the newly imported file. But when you overwrote it, LR didn't reread the metadata. You could file a bug report with Adobe, but my prediction is they'll classify it "as designed" (to minimize the number of open bugs and meet their management incentives) and ask you submit it as an "idea". In either case, I think it's highly unlikely they'll change such long standing behavior at this point.