Back at the launch of Rise of Shadows I had a pretty serious disconnect problem. I would get dced a minimum of 3 times a day, but it would go as far as 8 times. When I got disconnected I lost my connection to all Blizzard services - Hearthstone, the BNet Launcher, the Forums, everything. This lasted for weeks.
The Blizzard support team were very helpful and patient with my constant complaints. They asked me to do a ton of troubleshooting and unfortunately concluded, that the problem was not on their end. I was ready to buy a new router and demand that my ISP get involved, but before I did that I took a short break from Hearthstone for a couple of weeks and when I got back - NO MORE DISCONNECTS. Nowadays I get disconnected around once every 3-5 days and reconnect instantly, so I have not lost any games because of it.
So to everyone, who has such issues - I know how frustrating it can be; I know you should not have to deal with it; I know you just want to play the game, in which you have invested much time and maybe money. But if you really can’t resolve the disconnect issue, I want you to know that it may go away by itself.