I'm that unlucky Vladimir with the sound card problem.
"3000 words later..."
These are important words , but, anyway, probably I had to write a summary.
Speaking of the problem, I guess I found a "solution". These professional external audio interfaces, in order to minimize the latency while you're playing a musical instrument (a guitar, in my case), are using ASIO, bypassing the Windows sound sub-system. And, since usually they connect to a PC by using USB, I started to search for a problem thinking about USB ports.
Later, I noticed that in power options (USB settings), there's something related to a possibility to suspend USB ports. Of course, while using external audio interfaces, we want to avoid any interrupts in the path of the signal. So, I disabled it, but it didn't help. Then, I started to try different USB ports, since as far as I know, there might be problems related to providing all needed power by USB ports to connected devices (depends on a motherboard or a power supply). And fortunately, I found a USB port that allows me to use the external audio interface without killing the on-board audio. So, each time before I'm going to use the external audio interface, I switch the power plan to the "High performance", and connect the external audio interface to that "good" USB port.
I guess a USB hub with its own power supply can also solve this problem, but in the case when we want to remove any unneeded stuff from the path of the signal, I don't think that this is the "ideal" solution.
Also, in my email, I mentioned that everything was fine on Windows 7, and this problem started to occur only when I switched to Windows 8.
Larry, I also was thinking to write an email directly to Line 6, but I wrote to "Microsoft", because I have the same hardware, the same software, the same software versions and the same drivers that I had on Windows 7. I guess it's obvious that something was changed in Windows 8.
And I had a question in my email that wasn't answered here: How to correctly reboot the sound sub-system? Imagine, for some reason (bad drivers, software; it doesn't actually matter) it stopped working. How can I bring it back (without rebooting the OS (Windows 8))?