Since the GOTD team changed the search bar to search for non-giveaway software, it has been less convenient to search for actual giveaways. But because they didn't get rid of the regular search, you can still use it. Try this:
Copy-and-paste http://www.giveawayoftheday.com/?s= and enter your search term after the equal sign. It's that simple and you get the original search function back.
For Firefox users: add a search bookmark. Go to http://www.giveawayoftheday.com/?s=%s and press Ctrl-D. Put it into the Quick Searches folder. Go into your Bookmarks menu and find the new entry (under Quick Searches). Right click on it and select Properties. Give it a keyword, such as gotdsearch, and then click Save. Now whenever you type gotdsearch and a keyword in the address bar, it will search for giveaways, not random software.