3D Gaussian Splatting (3DGS) has recently demonstrated significant potential for streaming dynamic scenes, enabling the synthesis of photo-realistic and real-time free-viewpoint videos (FVVs). Conventional streaming pipelines optimize each frame independently, \textit{i.e.}, the attribute of the 3D Gaussians (3DGs) responsible for the static regions are supposed to be identical across all frames but are changed in the optimization process, thus causing temporal color inconsistency and visual flickering artifacts in the static regions. To tackle this, we propose CPOStream, which utilizes a prediction and observation module to determine the state of 3DG. Specifically, the prediction module records those 3DGs that are inactive in the past K frames and those would be ignored in the optimization process of the current frame reconstruction. Thus, the attributes of those 3DGs would be kept consistent across the past K frames, guaranteeing the temporal consistence. Additionally, the observation module conducts motion detection, and recognizes those new 3DGs which are not recorded in the prediction module and are first detected by the observation module in the past K frames. The attributes of those 3DGs are optimized during the current frame reconstruction. Experiments on multiple real-world FVV benchmarks show that CPOStream substantially reduces temporal flickering and improves reconstruction fidelity, achieving state‑of‑the‑art performance.