I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others", I'll repost your solution in case you'd like to "Accept" the answer.
Issue:
When configuring Azure AD Kerberos for Azure Files authentication, users should be able to mount Azure Files remotely without requiring a VPN. However, if file share permissions rely on NTFS ACLs with on-prem AD SIDs, the system may still need to contact the on-prem AD to verify permissions.
Solution:
The root cause was that the computer no longer had a local AD Kerberos ticket, which prevented it from verifying NTFS permissions to access the drive.
- Once the computer was able to contact the domain controller and receive a local Kerberos ticket, access to the drive was restored, even without an active connection to the domain controller.
- After testing, I found that the ticket remained valid for several days, allowing continued access to the drive without requiring reauthentication to the local DC.
If you have any other questions, please let me know. Thank you again for your time and patience throughout this issue.
Please do not forget to "Accept the answer” and “up-vote” wherever the information provided helps you, this can be beneficial to other community members.