Why won't my game save anymore?

My save function on single player seems to be completely gone.
I played for a while yesterday, yet when I opened the game today all my progress was lost and I was right back to where I started yesterday.

I have tried restarting. I have also advanced farther and saved the game again, yet when I exit the game and come back I always return to the same starting point, it never marks or saves my progress.

Is this a problem with the game or with the xbox 360?

I solved this problem for myself by not signing in until the game had started. Then, I signed in. When I loaded the last save, it went back to the save that I was unable to access before.

I think it's due to the CMOS battery in the Xbox being flat, which causes my Xbox to default to 22 November at 00:00 every time I turn it on, meaning that every time it saves, the date is older than a previous save.

This probably wouldn't be a problem if I connected to Live, but I can't do that as my PC won't allow it at the moment (it used to connect via my PC, and does connect via my girlfriend's laptop, but which is onerous)

If that's the problem, you can't do much about it other than delete all your save games every time you restart Portal 2 and load the most recent save (which may not be the save the Xbox says is most recent).