It's annoying to have Drupal QuickTabs revert to the default tab on every page load. There are a number of hacks out there that require changes to default ("core") files to make the last tab get re-selected on page refresh. However, the following fix will make the last tab re-select on page load. In my particular case I had 26 tabs, labelled A through Z, which each contained the same view, but with different parameters.
At the top of the view I included a Global PHP header with the following code:
thing = jQuery('#quicktabs-techspec').find('.active').find('.active').attr('id');
..which records the active tab (from my QuickTabs named "techspec") in a cookie. Then in the Panels page, where the QuickTabs were located, I included a panel with the following code:
tabName = "#" + jQuery.cookie("techspec-tab");
...which checks that cookie and "clicks" on the anchor which represents the last-used tab, bringing it again into the foreground.
Also, in this configuration, each tab will set the cookie only the first time it is clicked, on AJAX load. If you click back-and-forth the cookie will only retain the last "freshly-loaded" tab. But I think you get the idea.
Using this approach, and accounting for all the what-ifs, and even using sessions instead of cookies, you can come up with a solution that meets your particular use-case scenario to make your QuickTabs load the last-used tab on page refresh. Enjoy!