I've as well as many others here experienced disconnects from Blizzard games. I've had this problem for nearly 2 years. I did try to sort it out a couple times, but Virgin support is so incredibly useless, painful and downright horrendous time sink. I gave up. (Although was stupid enough to try a couple times...and man it is so excruciating painful. Virgin support must be the most incompetent irritating service we've ever encountered)
As it's only ever been a problem with persistent online games, more particular Blizzard games. And streaming Youtube, Netflix, Amazon has been perfectly fine. As well as downloaded huge amounts of data from Perforce has been fine. Only online gaming that disconnects me irregular, the past years I've just put up with it. But with Classic having launched I would like to see this problem solved. As well as since so many people have this problem I'm posting here, it gives exposure to this kind of problem. And maybe it will help. (If it gets sorted)
I also would like to try see this problem solved on final time as I'm moving house soon and if it's not resolved would switch provider.
Couple things that might be of use. I've tried both putting my hub in modem mode and router mode. In modem mode I used a netgear Nighthawk. I'm still on HUB2ac (I was meant to get a HUB3 when I moved to my current address and these issue's started. But I never got sent one. And when I tried solving it via support they tried selling me one. Thanks to a link on this forum I just ordered one (freeish) and maybe get one this time next week.
Those T3 timeouts don't look good, hopefully someone will look into it for you. How much of an interval between the timeouts is there, check your logs and see when it happens, is it a specific timeframe like every 1hr or is it sporadic and just randomly happens with no set timeframe?