Search result URL not working on multisite instance

I have a single Sitefinity instance with 3 sites.  (a site for North America, Europe, and Asia Pacific)

The site search pages on all of them are based on the same templates, and the search indexes are the same.

If I query the search index on the AP site, I get the following url in the browser:

/ap/search?indexCatalogue=site-search-ap&searchQuery=test&wordsMode=AllWords

And the links are proper in the search results. (/ap/<something>/<etc>)

If I query the search index on the EU site, I get the following url in the browser:

/eu/search?indexCatalogue=site-search-eu&searchQuery=test&wordsMode=AllWords

However, the links in the results are not working. They are missing the '/eu' from the generated urls. (/<something>/<etc>)

Now, the strange part.  If I query the EU search index from the AP search results page, I get working links.  If I go here:

/ap/search?indexCatalogue=site-search-eu&searchQuery=test&wordsMode=AllWords

I get proper URLs for the results (/eu/<something>/<etc>)

I have checked everything I can think of and everything is identical (pages, templates they are based on, search indexes) and I cannot figure this out.

Anyone have any ideas?