You have to play the required games every day or your Challenge Days will reset to 1. The required games will increase to 10 as you complete more Challenge Days. You can always see how many games are required and your progress at the top of the Challenges screen.
The Challenge Day changes when the time for the Daily Challenges runs out, and not necessarily when a new day begins in your time zone. Fun Run 2 Challenges reset at 10 am UTC. Use the countdown at the top of the Challenges screen to keep track.