Resolved
Reported for: Toolset Views 2.2.2
Resolved in: Toolset Views 2.3
A Views frontend custom search can update the results on the fly using AJAX. By default, it will also update the browser URL to include the bits coming from that search. However, when the custom search form contains a filter by post relationship, the bits about that filter will not get added to the URL.
This issue will be fixed in the next release of Toolset Views. On the meantime, this patch can be applied by unzipping it and uploading the two files it contains, replacing the existing ones in /embedded/inc/wpv-pagination-embedded.php and /embedded/inc/filters/wpv-filter-post-relationship-embedded.php.