So, the payment for my Xbox Gold was overdue so it was discontinued. Today I charged money to my Microsoft account. If I want to settle the bill now, it only appears to me Add new payment method. Now I have money in my account and can't pay with it.
Since you have a subscription that could not be paid because not enough credit, Microsoft requires an alternative payment method. Thus, they make sure that it does not come again to a payment default.
For a subscription more than understandable.
Although your question plus text does not imply that you want a solution, I still offer it.
Possible is Paypal which is set up quickly or a credit card. Alternatively, use Xbox Live prepaid cards instead of credit. Thus, you have no subscription and full control over the costs.
No card - no Xbox live.
These are available in retail for as long as 1, 3, 6 or 12 months at the same price as if you made it online. Even better prices can sometimes be achieved online. Since the cards / codes sometimes cheaper to get.