We tackle the problem of Persistent Independent Particles (PIPs), also called Tracking Any Point (TAP), in videos, which specifically aims at estimating persistent long-term trajectories of query points in videos. Previous methods attempted to estimate these trajectories independently to incorporate longer image sequences, therefore, ignoring the potential benefits of incorporating spatial context features. We argue that independent video point tracking also demands spatial context features. To this end, we propose a novel framework Context-PIPs, which effectively improves point trajectory accuracy by aggregating spatial context features in videos. Context-PIPs contains two main modules: 1) a SOurse Feature Enhancement (SOFE) module, and 2) a TArget Feature Aggregation (TAFA) module. Context-PIPs significantly improves PIPs all-sided, reducing 11.4\% Average Trajectory Error of Occluded Points (ATE-Occ) on CroHD and increasing 11.8\% Average Percentage of Correct Keypoint (A-PCK) on TAP-Vid-Kinetics. Demos are available at \url{https://wkbian.github.io/Projects/Context-PIPs/}.