The Daily Rewards are synced to the calendar month, and reset at the end of that month. This happens regardless of when in the month you first collected a Daily Reward. On the rewards calendar, you will see one more reward than there are days in the month; this is a preview of the first day of the next month.
If you miss a day of Daily Rewards, you will not skip a day ahead on the rewards calendar; you will continue to claim the next consecutive reward, meaning that you will lose your chance to claim one of the rewards later in the month.
If you are unable to log in on enough days during any given month, then it will limit the number of daily rewards you can claim. Be sure to log in every day to maximize your rewards!