Links in Global Site Search results omitting custom post type slug

When I do a global site search, the results returned don't have the CPT slug in the URL, so I am getting a 404 when I click the search result link. For instance, in my site a url looks like this:
http://siteurl/multisite-section/custom-post-type/post/,

but the link from a search result looks like this:
http://siteurl/multisite-section/post/

I have tried resaving my permalink settings and reindexing the site, but it hasn't worked.