When loading wow accounts from battle.net now have to wait until one account has loaded to the character selection screen before starting the second account from battle.net. Sometime late last year the ability to load both accounts at the same time broke.
What happens now:
Click play with first account and the wow window starts opening as it should.
Next change account in the battle.net window to other account and then click play.
The second wow window will try and load the first account which fails cause you cant have 2 windows of the same account open.
Loading first wow account window from battle.net then immediately changing to the second wow account in battle.net and clicking play both would load their correct wow account in their respective windows.