Bingo!
Your adapter is good.
But I believe you also installed BlueSoleil bluetooth stack/drivers that came with your adapter.
BlueSoleil does not support the full Joy-Con HID protocol. I tried it before and it was failing and causing the controller to disconnect also.
You need to replace the bluetooth adapter drivers with the Microsoft Bluetooth stack that comes with Windows.
(From device manager, right click the bt adapter and choose to update drivers. Then select the options that let you choose a driver from a list.)
If you still want to use some of the advanced features of BlueSoleil and still use the Joy-Cons,
try the Toshiba bluetooth stack. I believe it works with Joy-Con.
EDIT:
In windows 10 when you select the driver to install, the Microsoft Bluetooth stack is called Generic Bluetooth Radio or Adapter.
It's probably similar in windows 7