Edited by Blizzard: The information below should be followed after connection troubleshooting. The steps below are for a niche issue which is not common anymore
Thank you for your continued reports and also including what’s helped some of you out! We are still actively gathering reports for those who do contact us through the support site. Here’s a collective list of troubleshooting steps that have helped some folks.
- Temporarily uninstall any deck tracking software such as Innkeeper/Hearthsim
- Delete the Cache and Tools folder.
- Press Windows Key + R, and type in
%localappdata%and delete the Blizzard folder. - Reinstall Hearthstone.
- Create a New Admin account.
- Try an alternative connection.
- Try a testing on a Different region for the login, then switch back to the correct region.
- Remove any authorized applications such as deck tracking software in the Blizzard Account Settings, here.
It’s greatly appreciated for those of you who have shared your fix or workaround and I hope it helps those who runs across this thread 
Some of these suggestions will be specific to desktops, but some may be available on mobile devices as well to try out.
If the problem continues after these suggestions, please contact our Technical Support team. The reason why we request you to contact our team directly is because some of these issues may not respond to the above troubleshooting. These reports are also tracked on our end, so no need to worry about posting here as well!
We are leaving this thread open for any workarounds that are shared, and I’ll try to update this post for any new workarounds or information we can provide.