There's a bug where the auto-speedbrakes properly engage and then disengage in a fraction of a second. Otherwise put, they fail to engage. Here is a fix to the problem in xml and txt format. The xml file replaces the file in C:\Program Files\FlightGear 2.10.0.3\data\Aircraft\777\Systems or your equivalent.
Although your browser probably won't show the xml file as formatted xml, I include an xml and txt version in case I ever change the MIME settings in my Apache config file so that your browser does show formatted xml.
Significantly re-worked fix and page, 2013/08/24 - August 24
Original page 2013/04/07 - April 7