Ok, somehow things started working again. Not sure why my tests for wake did not work but this morning scheduled backup executed and it's scheduled for tomorrow too:
C:\WINDOWS\system32>powercfg /waketimers
Timer set by [SERVICE] \Device\HarddiskVolume4\Program Files (x86)\IDriveWindows\id_service.exe (IDriveService) expires at 7:30:00 on 21.12.2017.
Probably upgrade to 6.7.0.30 helped.