I just moved to a new apartment, and I popped Fallout 3 into my 360 before the cable company got around to turning my Internet service on. Before the move, when I did have an Internet connection, I completed two DLCs (The Pitt and Broken Steel); I had some items and side quests left over from those (spoiler: e.g. the gun The Infiltrator and the side-quest about selling cameras to the BoS).
After the move, I opened up my old save file and wandered around the DC Wasteland some, but didn't do any quests. I then saved and turned off my 360. My Internet service was turned on the next day. After that, when I opened my save file, it looked like I had never completed either DLC; the unique items were not in my inventory and I was hearing Wehrner's Distress Signal again.
How can I get my items back? Or, if that's not possible, how can I play Fallout 3 while not connected to the Internet without losing my progress?