The price to enter the Challenges resets after a few days so you don't have to spend extra diamonds to participate.

The following is how long it takes until the fee resets for each Challenge:

Tier 2 - resets after 5 days
Tier 3 - resets after 8 days
Tier 4 - resets after 11 days
Tier 5 - resets after 14 days
Tier 6 - resets after 28 days
Tier 7 - resets after 42 days
Tier 8 - resets after 42 days