I'll state this, Blizzard has some issues with some computers for whatever reason. I know this because my main computer has this issue. I have about 6 computers in the house on the same network, but only my main one ever has disconnection issues. I've reloaded from scratched windows and drivers on every machine multiple times. Changed out tons of various hardware. The only machine that sucks with Blizzard is my main one and the only thing I can think of is that Blizzard doesn't like the nic or motherboard for my main pc. I can play any other game with my main pc online for hours on end. No DC issues. But when it comes to Blizzard games it's a crap shoot. Some nights I can play with zero disconnects. Some nights it is every 5 minutes. It's annoying because I can be running hearthstone from 3 or 4 different machines and ONLY the main one disconnects. Trust me I've tested this out in every possible conceivable way there is. Which include:
Taking all computers to a friends house for same results.
Fresh installs of windows which include vista, 7, 8, and 8.1 to try them all.
Various version releases of all the drivers available for my hardware.
Hardware changes to include memory, cpu, psu, and harddrives (only thing constant is my p67 pro fatality board on my main pc)
Different routers and network configurations as well. Wired and wireless connections included.
So the point being is don't bang your head like I did trying to figure it out. Also, don't count on Blizzard because they won't care. Hopefully you don't have the same p67 motherboard and or on board nic that I have.