First, make sure that you’re running the latest version of the EggBot software (which is included with the AxiDraw software installer).
Next, disconnect the EggBot — both power and USB. Restart your computer. Plug in USB only, not power, for the moment. Open Inkscape, and try and connect.
If you still aren’t able to connect, try a different USB cable if you have one available, and/or a different port on your computer.