Sorry if this is a dumb question, but you're not doing patrol missions are you? If so, those are meant to come back after 10-15 minutes, so if you quit for the day (or even just go back to orbit) they will all come back, but you haven't actually lost any progress.

The game is an online interactive, connected game. If you are idle for a certain amount of time it will kick you off the servers because it increases the server load when you are just sitting there idle and not playing. Most items that you play in game (especially story missions) should be able to be completed in <45 minutes each so I am not sure why you are having to start and stop so much. You do a mission, you complete the mission, you move to the next mission. There is no manner to 'save progress' as you go along so you can return to a point that you were just at a later point. You have to physically get back to that point. I am still not understanding how you could be spending THAT much time that you need to take breaks, etc. unless you are doing RAIDS or PoE at high levels. But even that, with a decent group, you can blow through a raid in <1 hour and Skolas in an hour or so. Maybe you can clarify a bit what mission you are in that is taking you THAT long to complete so we can assist pointing you in the PROPER direction to avoid wasteful time spending.

Hi there, I didn't quite understand the question. Are you referring to returning to the start screen when you log out? If so, I can provide an explanation. Internet connection is required to play Destiny. When you turn your console off, your internet connection is disabled. Destiny is therefore no longer to keep you in game without internet connection. Hope this helps.