The driver version 3345 has been tested on sleep and hibernation mode. I would recommend getting different video drivers from your motherboard maker, as they may be customized for your motherboard model.
Check here for drivers for your motherboard model:
@allan_intel: Thanks for the reply. But those are just older versions of original Intel drivers bundled by ASUS for convenience - nothing really specific. Actually they issue a warning that never drivers will be overwritten.
And, btw, I had those installed, when the problem started. I only installed the newer drivers from the Intel site hoping that would fix the problem - it didn't change a thing.