I don't know what your issue could be, but I'll tell you my experience with Logitech.  I've used their headphone, speakers, and keyboards for many years.  This was with the software they had before G Hub.  Never had a problem.  Once I was forced to use G Hub to control things, I had nothing but problems like settings not being loaded at a fresh boot up, random disconnects/reconnects of the head set etc.  I finally gave up and stopped buying Logitech headphones and keyboards.  I still use the 2.1 sound system though since you don't use G Hub for that.
 
I always liked their gear, it was pretty decent quality for reasonable prices.  It was the software that ruined it for me.  It's been several years now since G Hub came out, I don't know what it's like these days.
 
Your issue sounds a bit more severe than mine were.  Hope you figure it out.  GL