Hi there, thetaracer.
Thank you for visiting the QuickBooks Community. I'll share some details on how invoice payments work when using QuickBooks Payments. Then, to ensure you're able to see the entry as paid in the QuickBooks Desktop software.
When you have QuickBooks Payments and your customers pay their invoices online by credit card or ACH bank transfer, there's a specific time for payment to deposit. The customer payment usually reaches your deposit bank account within 2-3 business days of the transaction. It can also vary on how long it takes the bank to verify and process electronic deposits. With this, once payment has been applied to an invoice, its status will automatically show as paid.
If you're a new user, we deposit your funds within five business days after your first payment. Your first deposits take a bit longer while we set up your merchant account. Then, once payment has been applied to an invoice, its status will automatically show as paid. That said, it could be the reason why invoices are still showing as open in the QBDT system.
If the invoice is still shown as open within the given length of time, I suggest closing and reopen your QuickBooks Desktop. This is to ensure that you can start using the system with a clean slate and to see the latest data you have in your company file.
If the issue persists, I reccomend updating QuickBooks Desktop to the latest release to keep your software up-to-date so you always have the newest features and fixes. You can click this article to see steps on how to perform the process: Update QuickBooks Desktop to the latest release.
Please also refer to this article to see how QuickBooks Payments deposits work in QuickBooks: Common questions about payments deposits in QuickBooks Online.
Don't hesitate to post again here in QuickBooks Community if you have additional questions. I'll be right here to help. Have a great day!