I tested this on 3 different computers (both desktop and laptop, with both built-in and USB dongle bluetooth modules) and it always connected fine for me with the Wii remotes I have available. The only thing I know could impact this is user privileges so the only thing I can think of you could try is to run Gamepad Phoenix as admin (by right-clicking GamepadPhoenix.exe and selecting "Run as administrator").
Do you have any other programs that can communicate with a Wii Remote?