Having the same issue. Original Xbox, MFG date: 8-1-2006, 120 GB HD, XBOX Live Gold Member, connected to the internet via wifi.
After I finished episode 1 and tried to continue to episode 2, the game loaded back to the begining of episode 1 again. Tried to continue from my save, which brought up the episode 2 menu, but again episode 1 restarted. Tried several different combinations of loads / save / loads, no luck. Then I went into the games menu on my xbox dashboard and notice that there were 2 the walking dead games showing up, one with achievements, one without. I started the one that showed the achievements, and bam, espisode 2 loaded correctly. Not sure if that is what got it rolling, but it was the last thing that I did before it worked correctly.
Then, Finished espisode 2, but the game froze on the progress report at the end of the espisode. I was able to bring up the xbox menu and cycle through, so I know the xbox itself didn't freeze. I had to restart the game to get things moving again, loaded my save file, tried to continue with episode 2 to start espisode 3, and un-bam, back to the start of episode 1 again. Tried the same game menu trick of earlier, but no luck this time. Even when I try to rewind to replay the last part of episode 2 again, the game loads, then back to the start of episode 1 again. If i try to look at the progress info from episode 2, a blank page shows up and the game freezes again everytime. Out of idea's this time. Any thing I can try to help you guys figure out what is going on please let me know, thanks