You would need to activate two features: Commission groups and Performance rewards.
Let's say, that you would like to give at most 5 commissions in total for each affiliate in the actual month. If more sales are made through that affiliate, the commission would be zero until the next month starts.
Navigate in the Merchant panel to Campaigns -> Campaign manager -> edit Campaign -> Commission groups -> Add group. Let's call this group ZERO.
Click Edit at the 'per Sale' commission and set $0 or %0 commission. Click Save.
Next, for the same campaign, click Performance rewards -> Add rule.
Set conditions: if the value of commissions that are approved in the actual month is higher than $10
Set Action: then add affiliate into commission group
Select: ZERO
As you can see there are several options (different time - month, year, week, all time, apply for commissions or sales or total cost, etc.).
If this is set, affiliates would normally earn commissions for sales until they earn more than $10 in the actual month. After that, only 0$ commissions would be assigned to them until the next month starts.