We had a similar problem and solved it by purchasing a power bank. It charges from the kobuki base, provides 19V to the NUC and does not kill the Kobuki battery. We use one of the 19V connectors on the back of the Kobuki and make an adapter to charge the powerbank when the robot is on the charger.
This is the one we used: https://www.amazon.com/RAVPower-23000mAh-Portable-Charger-External/dp/B00HFMUBYG/ref=sr_1_1?ie=UTF8&qid=1445870672&sr=8-1&keywords=ravpower+23000