asking why it is still Unassigned for many days.

I understand your frustration with your support case remaining unassigned for several days without a response. This is not the typical experience AWS aims to provide.

Based on similar situations, there appears to be an occasional pattern where billing support cases can remain unassigned for extended periods - sometimes up to 3-6+ days without responses. This is particularly concerning for billing-related inquiries which typically should receive priority attention.

For your specific case regarding a refund for accidental AWS Business Support charges, the delay is unusual but not unprecedented. Here are some insights on what might be happening:

1. There may be a backlog in the support queue for billing and account issues.
2. Your case might require specialized review that's taking longer than expected.
3. There could be a system issue affecting case assignment.

While waiting for a response, here are some suggestions:

1. Update your existing case to request a status update rather than creating multiple tickets, as having several open cases on the same issue might actually slow down the resolution process.
2. Check all email addresses associated with your AWS account, including spam folders, for any communications from AWS.
3. Ensure all your contact information in the AWS account is up-to-date.
4. Consider requesting a call or chat on your case. This option looks to connect you to account and billing support to discuss your case further and is normally recommended for time sensitive cases. More info can be found here: go.aws/phone-support.

AWS Support representatives who have responded to similar situations on public forums have acknowledged these delays and typically escalate such concerns internally when they become aware of them. Rest assured that even though your case is showing as "unassigned," it should still be in the queue for review.
Sources
AWS Support not responding - 2 days | AWS re:Post
URGENT: Multiple Unassigned Support Tickets for Account Verification - 3+ Days Without Access | AWS re:Post
AWS Support not responding on suspended account | AWS re:Post
AWS Support Has Abandoned 4 Billing Cases - All Unassigned - Student Account Ignored | AWS re:Post
Charged for Support (Business) while on free tier and basic support plan | AWS re:Post