I had the same problem with a Bose Lifestyle 35 system and a DirecTV HD20-100 set top box. I called the Bose 800 Number, explained the problem and they recommended Code 1377 as others have reported. My system did NOT list this code. They talked me through verifying the software versions in my system, which SHOULD HAVE HAD the 1377 code in it. They sent me a software update DVD for my Lifestyle 35, anyway, which I used to update my system, and voila!!
Now my Bose remote controls my DirecTV HD20-100 box along with everything else in my home theater setup.
Call the Bose 800 number which can be found on the http://owners.bose.com
Don't take no for an answer, make them send you the DVD software update -- I doubt they will resist -- they were very polite and helpful to me.
Good Luck -- CALL THEM.