It looks like a fix is on the way for those that are having DRM troubles. Currently, when XBLA games are purchased they lock themselves to both your console and gamertag. As long as you are playing the game on the console that it was purchased on, you can be offline or even on another profile and have access to your games. However, if a game detects that it is running on a different console then the one they were purchased on, it will require you to log into Xbox Live with the gamertag that they were purchased on to verify that you did in fact buy the title.
For many people this has never caused a problem. But those that cannot stay connected to live and have switched consoles (perhaps due to the Red Ring of Death) have been unable to play their games. This has been a problem for years, but it looks like Microsoft is finally stepping forward with a solution. In an interview with Next-Gen, Microsoft’s Marc Whitten says that, while there won’t be a traditional “Spring” Dashboard update, “the team will be releasing a new digital rights management (DRM) tool next month that will allow you to better consolidate your licenses for downloaded content to a single Xbox and allow you the freedom to be able to play your content both online and offline.”