You can tell how much time you have left in a contest by looking at the black bar below the contest on the main Sweeps page. There it will list many days and hours there are left until the contest ends. For example, if there are 7 days and 21 hours left it would be displayed as "7d 21h."
When you tap on a contest to select it, you are delivered to the redemption page. On that page you can see how much time is left in the contest listed in the upper right corner.