I compared the successful login and the failed login event messages and I think I found the cause of the issue:

Successfull login (all below are svservice events):

1. Session ID: 1
2. Manager: <appvolmgrfqdn>, Status: 200 Response (488 bytes): *1*#1#LOGIN <domain\user> MOUNTED-WRITE;vsanDatastore\appvolumes\writables\<domain>!5C!<user>.vmdk;{3b8eee5c-9d57-4463-af26-355fa89a59af} ASYNC WRITABLE-REBOOT;Volumes were not mounted due to an issue with your Writable Volume. Please try logging in again, or contact your administrator. SET-VAR;WRITABLE_FAILURE_ACTION;REBOOT SET-VAR;WRITABLE_FAILURE_MESSAGE;Volumes were not mounted due to an issue with your Writable Volume. Please try logging in again, or contact your administrator.
3. Action: mounted Path: \Device\HarddiskVolume3 GUID: {471C5721-0000-0000-0000-100000000000} VolumeId: {3B8EEE5C-9D57-4463-AF26-355FA89A59AF}
4. Manager: <appvolmgrfqdn>, Status: 200 Response (2 bytes): No
5. Action: mounted Path: \Device\HarddiskVolume3 GUID: {471C5721-0000-0000-0000-100000000000} VolumeID: {3B8EEE5C-9D57-4463-AF26-355FA89A59AF}
6. Event: [prestartup] Volume Path: [\SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\]
7. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\PRESTA~1.BAT WaitMilliseconds: -1
8. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\PRESTA~1.BAT WaitStatus: 0, ExitCode: 0
9. Event: [startup] Volume Path: [\SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\]
10. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\startup.bat WaitMilliseconds: -1
11. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\startup.bat WaitStatus: 0, ExitCode: 0
12. Path: \Device\HarddiskVolume3 GUID: {471C5721-0000-0000-0000-100000000000} SystemVolume: 0)
13. Installing fonts Event: windows_install_fonts Path: \SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\
14. Refreshing desktop
15. Session ID: 1
16. Path: C:\Program Files (x86)\CloudVolumes\Agent\svservice.exe deskmon 1 WaitMilliseconds: 0
17. Event: [shellstart] Volume Path: [\SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\]
18. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\SHELLS~1.BAT WaitMilliseconds: -1
19. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\SHELLS~1.BAT WaitStatus: 0, ExitCode: 0
20. Checking provisioning state Event: appcapture Path: \SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\

Failed login (all below are svservice events):

1. Session ID: 2
2. Manager: <appvolmgrfqdn>, Status: 200 Response (488 bytes): *1*#1#LOGIN <domain\user> MOUNTED-WRITE;vsanDatastore\appvolumes\writables\<domain>!5C!<user>.vmdk;{3b8eee5c-9d57-4463-af26-355fa89a59af} ASYNC WRITABLE-REBOOT;Volumes were not mounted due to an issue with your Writable Volume. Please try logging in again, or contact your administrator. SET-VAR;WRITABLE_FAILURE_ACTION;REBOOT SET-VAR;WRITABLE_FAILURE_MESSAGE;Volumes were not mounted due to an issue with your Writable Volume. Please try logging in again, or contact your administrator.
3. Action: mounted Path: \Device\HarddiskVolume4 GUID: {471C5721-0000-0000-0000-100000000000} VolumeId: {3B8EEE5C-9D57-4463-AF26-355FA89A59AF}
4. Action: mounted Path: \Device\HarddiskVolume4 GUID: {471C5721-0000-0000-0000-100000000000} VolumeId: {3B8EEE5C-9D57-4463-AF26-355FA89A59AF}
5. Event: [prestartup] Volume Path: [\SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\]
6. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\PRESTA~1.BAT WaitMilliseconds: -1
7. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\PRESTA~1.BAT WaitStatus: 0, ExitCode: 0
8. Event: [startup] Volume Path: [\SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\]
9. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\startup.bat WaitMilliseconds: -1
10. Path: C:\PROGRA~2\CLOUDV~1\Agent\Config\Default\UIA_PL~1\startup.bat WaitStatus: 0, ExitCode: 0
11. Path: \Device\HarddiskVolume4 GUID: {471C5721-0000-0000-0000-100000000000} SystemVolume: 0)
12. Installing fonts Event: windows_install_fonts Path: \SnapVolumesTemp\MountPoints\{471C5721-0000-0000-0000-100000000000}\
13. Refreshing desktop

And then it follows (User Profile Service events):

1. Access is denied. C:\Users\<user>\ntuser.dat
2. Access is denied
3. The system cannot find the file specified

Therefore I came to the conclusion that the writable volume content is unaccesible due to wrong permissions.

Now to figure it out why and how to solve it.