Xbox 360 games memory problem?

If I download a 360 game at game pass, I can start it. The message "separated from xbox live" appears on the loading screen. Since you have to connect to xbox live to save, I can play the games but not save them. At xbox one I can still play online without any problems. My question is can you fix that

The problem doesn't come to me. I don't have to register to play Oblivion, for example.

* And to save.