Here’s the non-working scenario:
You initiate a search from the ‘default’ search at the top, in the Master Page, and you get no results. You end up on the correct results page, and then it works when you click on the search box within that page. If it’s going to the correct search results page, technically, it should be working correctly. So, if it’s not – try doing the following:

Go into Site Actions/Site Settings, and under Site Collection Administration, click on Search Settings.

In the Site Collection Search Dropdown Mode section, change the dropdown from:
Do not show scopes dropdown and default to contextual scope
Do not show scopes dropdown, and default to target results page.

Hopefully, that will work for you.