If a customer has an existing credit, it will apply to their invoices, Gwillcon. I'll be glad to explain this process in detail.
Please know that QuickBooks Desktop doesn't have a feature that marks invoices as automatically paid. However, if you issue a credit memo for your customer and save the transactions, the Available Credits prompt will appear.
If you accidentally select Yes when the prompt appears, the credit memo will be applied, which offsets the total amount due and automatically marks the invoice as paid.
For further reference, I have attached a screenshot below:

Here's an article that you can save if you want to notify your customer about their balances that may soon become overdue: Create and send customer statements in QuickBooks Desktop.
Feel free to comment down below if you have other concerns or question about customer payments and invoicing, Gwillcon. We'll be around to guide and assist you.