Tracking and manipulating irregularly-shaped, previously unseen objects in dynamic environments is important for robotic applications in manufacturing, assembly, and logistics. Recently introduced Gaussian Splats efficiently model object geometry, but lack persistent state estimation for task-oriented manipulation. We present Persistent Object Gaussian Splat (POGS), a system that embeds semantics, self-supervised visual features, and object grouping features into a compact representation that can be continuously updated to estimate the pose of scanned objects. POGS updates object states without requiring expensive rescanning or prior CAD models of objects. After an initial multi-view scene capture and training phase, POGS uses a single stereo camera to integrate depth estimates along with self-supervised vision encoder features for object pose estimation. POGS supports grasping, reorientation, and natural language-driven manipulation by refining object pose estimates, facilitating sequential object reset operations with human-induced object perturbations and tool servoing, where robots recover tool pose despite tool perturbations of up to 30°. POGS achieves up to 12 consecutive successful object resets and recovers from 80% of in-grasp tool perturbations.