Although machine learning holds an enormous promise for autonomous space robots, it is currently not employed because of the inherent uncertain outcome of learning processes. In this article, we investigate a learning mechanism, Self-Supervised Learning (SSL), which is very reliable and hence an important candidate for real-world deployment even on safety-critical systems such as space robots. We introduce a novel SSL setup that allows a stereo vision equipped robot to cope with the failure of one of its cameras. We present preliminary results from an experiment on the International Space Station (ISS) performed with the MIT/NASA SPHERES VERTIGO satellite. The presented experiments were performed on October 8th 2015 on board the ISS. The main goals were (1) data gathering, and (2) navigation on the basis of stereo vision. First the astronaut Kimiya Yui moved the satellite around the Japanese Experiment Module to gather stereo vision data for learning. Subsequently, the satellite freely explored the space in the module based on its (trusted) stereo vision system and a pre-programmed exploration behavior, while simultaneously performing the self-supervised learning on board. The two main goals were successfully achieved, representing the first online learning robotic experiments in space. These results lay the groundwork for a follow-up experiment in which the satellite will use the learned single-camera distance estimation for autonomous exploration in the ISS, and are an advancement towards future space robots that continuously improve their navigation capabilities over time, even in harsh and completely unknown space environments.