Not sure if my pen (adonit touch pixel) is having charging issues but it disconnect after a few seconds despite having a green light when on it's charging dock. I looked into the settings and it shows that I'm using an iPad Pro and the format cannot be changed. It is locked and cannot be changed to iPad Air 2, the device I am using. Not sure if the issues are related but thought I'd throw it out there.
I've never heard of a stylus being "locked" to a particular device. Have you tried force-quitting Draw then relaunching the app and trying again to connect your stylus?