Fist I would like to mention that its a good idea to use high quality USB cables... But I doubt that is the source of your problem.
I have a similar problem with my 64S after I updated to the most recent Universal Control (22.214.171.124879) and 64S Firmware (126.96.36.199872). I would first encounter intermittent signal then it would go out completely. Then the 64S would stop responding to the computer. I opened a ticket with Presonus and the resolution was to switch the 64S to Compatibility Mode. I switched it back to 64 Channel Mode and it continued to work. It fixed the problem initially but days after, it lost connection again. I switched modes again and it started to work again.
This is very frustrating. It appears that the drivers for Studiolive Series III is very unstable. The most stable firmware I've experienced is Firmware V2.4 along with Universal Control V3.4. I'll give this current version a couple more weeks of experimentation but I'm afraid I may end up rolling back to the older more stable version.
Presonus, if you're listening, please give us stable USB drivers for our mixers.
zberto, I hope this helps. What version of firmware and Universal Control are you running?