Some search types can be too long and that’s why mobile search replaces header search after certain resolutions. The mobile search is closed by default and when click to open it shows all fields

To hide mobile search and show the header search you will need custom css:

This css may need to be adapted to your search type

#adv-search-header-mobile {
display: none;
}

.adv-search-1 {
display: inherit;
}

.adv_extended_options_text {
margin-top: 10px;
}