Hi! The game autosaves every 10 minutes (unless you turn that off), and you can do manual saves either by going to the main menu and selecting save, or by pressing the quick save button. What exactly is the problem that you're experiencing?
Going to the save menu shouldn't be closing the game.
Can you send me a copy of the game log from a play session where you've tried to save from the main menu to the address listed under the "Technical help" section here on the store page (instructions on where to find logs are in the "Log, save, and config file locations" section)?