Days advanced, ribbons, and profile experience are all saved. Your squad does not carry from session to session. Whenever you choose to halt, you will lose your squad, starting over with a brand new 6 man squad on the next session.
But if you choose to advance (when you finish a mission)(I forget what the actual word is but it is the other option) you keep your squad, but if you die you lose all of your progress that you gained with that squad. It is all explained when you mouse over the options.