I just recently purchased the game on Xbox Live Arcade today. I played through the first episode and got to chapter 4, when I got killed. Sorry, not perfect. I was pretty dismayed when I pushed "A" on the death screen and went all the way back to the game menu screen. It then asked me to load up a completely new game. None of my progress was saved. I played again to Chapter 3, and then quit out the game. Again, none of my progress was saved.
Now, the game does not ask me what storage device I would like to save to, Hard drive or Cloud, when I push start to load up the game. When I select "Play", the next screen is to pick "Standard" or "Minimal". Then I select what episode I want to play. If I push "B" to go back from this point, it now lets me select one of the three save file slots which I was not previously allowed to select, but even if I select one of these and play through, no progress is saved. I tried.
I have tried deleting the game from the Hard Drive and redownloading it. I also cleared my system cache, which allowed me to get an update, but after downloading the update, it booted me out of the game and into the dash. I should also mention that when I got kicked from Xbox LIVE, I got an odd message I had never seen before.
"Disconnected from Xbox LIVE
Reconnect to continue: 10 minutes remaining"
And the normal update message appeared, but it doesn't usually give me a message stating this. But even after downloading the update, the game still did not function properly with the save system.
Finally, I am in the latest Xbox LIVE beta test for the fall update, so this very well may be an issue with that. But I don't know if that is something you have to look at on your end, or if I should contact MS about this. Thank you.