The workaround seems to be starting the Studiolive 16.0.2FW before connecting it with Firewire - cable to PC. Then connect the cable, and everything works as should. But of course it would be nice that the cable could be always connected, and not needed to unplug/plug every time Studiolive is started.
I'm using StarTech PEX1394B3 - PCIe - card, which should be compatible with Studiolive acc. to info found here in Presonus - site.