Hello,
If it is not the "Dynamic display" setting, the cause is the AJAX refresh of the filters: when you click "Filter", HikaShop reloads each filter block in the background, but on your SEF setup that background request returns the full page instead of only the filter block. The script then puts the wrong block (your search box) in place of the Material / Volume / Family filters, so only the search filter stays visible.
A normal full page reload of the same filtered URL shows all the filters correctly, so your products and your filters are fine, only the AJAX refresh path is affected.
I've made a patch on our end which should help. Download the install package of HikaShop on our website and install it on yours in order to get the patch. It should then work properly.