Whitewater I have the exact same problem. Some times I get it to connected state and can transfer data successfully but then other times it just doesn't work.
I haven't figured out what's wrong yet. I've had varying degrees of success on different devices. One sketch would work fine with bi-directional communication on one device but only unidirectional on the other. Another sketch would work on both. Today I only had one successful run out of perhaps ten or fifteen attempts with different very simple sketches.
I always lose packets when I try sending them them too fast from the Due, like three in a row without any time between.
And the power is weird, isn't it? Of course it should power the USB port even if it's running on an external power source!