The WPFTS Pro version you are using is very outdated. Please consider upgrading to 2.46.x which is the latest. It has a completely new indexing and searching algorithm and it should solve your issue.
It didn't work at first but I found the problem. The WPFTS Add-on for WP Download Manager wasn't passing the $is_enable_external_links parameter to GetCachedFileContent_ByLocalLink, so it wasn't indexing the WPDMPRO external files.
I changed that, and it did index everything. However, the performance on the WPDMPRO front-end pages was unbelievably slow. It turned out, it was reindexing every file any time it's post was viewed through the front end. So, I set $is_force_reindex to false in the call to GetCachedFileContent_ByLocalLink, and that seemed to fix it.
I don't know whether the changes I made to my copy of the the WPFTS Add-on for WP Download Manager were correct, but there are definitely some changes required there to make this work.
It does appear that this functionality will work as long as WPFTS Add-on for WP Download Manager is updated.
It happens because you have problems with wp-cron tasks or DNS configuration.
If you have your website hosted locally, often the domain name is just recorded in /etc/hosts file. This is normally okay for browser access (and this is why indexing is coming well but slow when your WP admin is open). But PHP can not read /etc/hosts by some reason and thus indexing procedure can not go internally.