Hi,
no I haven't get any response from support. In the meantime updated to Mac OSX 10.9.1 and use ESET Cybersecurity 5.0.115.0. I had reinstalled ESET but same problems.
Last 5 fresh boot periods ESET wasn't working in 3 boots. One problem was that I didn't always realize that it don't work so my system is not unprotected. I had to manually start ESET daemon by terminal via
sudo /Applications/ESET\ Cyber\ Security.app/Contents/MacOS/esets_daemon
Then I could start the ESET Cybersecurity App. Before this it will not start. In the Tools->Log there are no details about that.
Please help me out.