It works as this:
You win a game, you'll be rewarded Stigma. The amount depends on your performance.
When looking at the antagonist league in the main menu you'll find yourself in the list with the rank (Icon with a number to it) you will be rewarded -at the end of the season (a week)-.
Check the timer on the upper right on that screen to know when the qualification ends.
This timer resets every week and so does the league.
The first 20 Stigma you gather will be kept, no matter how often you lose but everything above 20 Stigma will be cut if you lose. The screen at the end of your mission gives more info on how much Stigma you (would) lose.
IMPORTANT:
Once you are rewarded a rank, you'll only get to keep it for one week!
In other words: You will be rewarded a rank -every- week, even when you haven't gotten a single Stigma.