You have the wrong ID for the larger search bar. This is what you had it look like:
<input type="search" title="Search for:" name="s" value="" placeholder="Search …" class="search-field" id="search-terms" />
Change the ID from "search-terms" to just "search":
<input type="search" title="Search for:" name="s" value="" placeholder="Search …" class="search-field" id="search" />
When I did that on jsfiddle it worked flawlessly.