Thanks for reaching out to the Community, jlk2021. I appreciate your detailed information.

Since you're receiving a "QuickBooks is unable to log in to your Intuit Account at this time. Please try again later." error message after signing in to the Intuit Account with your multi-factor authentication code, I'd recommend confirming the code wasn't expired. If you wait too long, your code could expire, then you have to generate a new one by using the resend code option.

In the event you've already confirmed your code wasn't expired, and it continues occurring with other non-expired codes, you'll want to get in touch with our Customer Care team. They'll be able to pull up your account in a secure environment, conduct further research with you, and create an investigation ticket if necessary.

They can be reached while using QuickBooks.

Here's how:
 

1. In your top menu bar, go to Help, then QuickBooks Desktop Help.
   
   
    
2. Click Contact Us.
   
   
    
3. Enter a brief description of the issue in our Ask a question (or tell us what's wrong) field, then hit Continue.
   
   
    
4. Select We’ll contact you for a callback or Message Us to start an instant messaging session.

Be sure to review their support hours so you'll know when agents are available.

I've also included a detailed resource about working with multi-factor authentication which may come in handy moving forward: Verify your Intuit Account with multi-factor authentication or two-step verification

I'll be here to help if there's any additional questions. Have an awesome day!