As a primary stage of connected and automated vehicles (CAVs), the cooperative adaptive cruise control (CACC) system takes some outstanding advantages such as accurate perception and timely reaction, which benefit from vehicular communication, over human-driven vehicles (HDVs). However, these advantages will turn into stability risks in case of communication failures caused by malicious attacks. Thus, this study aims at analyzing the stability of heterogeneous traffic flow with communication failures. We model two types of communication failures: bogus messages and transmission delay, and introduce drivers’ takeovers to react to communication failures. As a result, heterogeneous traffic flow consists of normal CACC vehicles, CACC vehicles with communication failures, and HDVs. Then, a series of numerical analyses, including startup and braking analysis, incidents analysis, and density wave, are proposed to verify the theoretical models and demonstrate their major properties. Besides, a discussion on traffic capacity is presented to analyze the overall impact of communication failures on traffic flow characteristics. The findings can help to investigate the stability evolution of heterogeneous traffic flow and determine the appropriate traffic flow configuration under communication failures.