BuddyPress.org

Or you can try to access to some page in WordPress admin area (e.g.: with an ajax call) ?

BuddyPress doesn’t do this by default. Considering you can’t reproduce, I expect the client is using custom code that’s causing the problem (either in their functions.php file, bp-custom.php file or in an activated plugin). Check those 3 locations on your client’s site for anything strange.