We introduce a novel robotic system for improving unseen object instance segmentation in the real world by leveraging long-term robot interaction with objects. Previous approaches either grasp or push an object and then obtain the segmentation mask of the grasped or pushed object after one action. Instead, our system defers the decision on segmenting objects after a sequence of robot pushing actions. By applying multi-object tracking and video object segmentation on the images collected via robot pushing, our system can generate segmentation masks of all the objects in these images in a self-supervised way. These include images where objects are very close to each other, and segmentation errors usually occur on these images for existing object segmentation networks. We demonstrate the usefulness of our system by fine-tuning segmentation networks trained on synthetic data with real-world data collected by our system. We show that, after fine-tuning, the segmentation accuracy of the networks is significantly improved both in the same domain and across different domains. In addition, we verify that the fine-tuned networks improve top-down robotic grasping of unseen objects in the real world.