You can individually edit the next payments for customer's membership. To do this go to the Customer profile >> Customer's membership tab >> select the membership you wish to edit >> select the upcoming payments tab.
Pick the payment you want to edit and you will be taken to a page to edit that individual payment. Here you can change the bill amount, change the dates (useful if the customer wants to delay payment for a particular month), skip this payment, initiate payment early, and you can also edit the description for this one payment to contain an explanation.
You will then see the changes on the upcoming payment tab.