Cooperative perception (CP) enhances situational awareness of connected and autonomous vehicles by exchanging and combining messages from multiple agents. While prior work has explored adversarial integrity attacks that degrade perceptual accuracy, little is known about CP's robustness against attacks on timeliness (or availability), a safety-critical requirement for autonomous driving. In this paper, we present CP-FREEZER, the first latency attack that maximizes the computation delay of CP algorithms by injecting adversarial perturbation via V2V messages. Our attack resolves several unique challenges, including the non-differentiability of point cloud preprocessing, asynchronous knowledge of the victim's input due to transmission delays, and uses a novel loss function that effectively maximizes the execution time of the CP pipeline. Extensive experiments show that CP-FREEZER increases end-to-end CP latency by over $90\times$, pushing per-frame processing time beyond 3 seconds with a 100% success rate on our real-world vehicle testbed. Our findings reveal a critical threat to the availability of CP systems, highlighting the urgent need for robust defenses.