We've been battling this issue for about 6 months and I've made some progress on it recently.
We checked all the same things as you've already checked.
What we observed was if a machine was rebooted and you logged in and tried to access the SYSVOL volume you would get a credentials prompt. You could try any credentials and it would always fail basically making the SYSVOL inaccessible! NETLOGON was fine though. If you leave the machine for an hours SYSVOL suddenly then becomes available again.
A lot of forums will point you down disabling UNC hardening, we didn't want to do that for security reasons so I persevered and eventually stumbled across 3 registry keys that have eradicated the issue for us.
Hive:HKLM\SYSTEM\CurrentControlSet\Services\NlaSvc\Parameters
Value: AlwaysExpectDomainController
Type: REG_DWORD
Data: 1
Hive:HKLM\SYSTEM\CurrentControlSet\Services\Dnscache\Parameters
Value: MaxNegativeCacheTtl
Type: REG_DWORD
Data: 0
Hive:HKLM\SYSTEM\CurrentControlSet\Services\Netlogon\Parameters
Value: NegativeCachePeriod
Type: REG_DWORD
Data: 0
It may not be the same for you or suitable for your environment but may be worth trying the above in a tiny controlled test and see how you get on.