Vehicle-to-vehicle communications can be unreliable as interference causes communication failures. Thereby, the information flow topology (IFT) for a platoon of connected autonomous vehicles (CAVs) can vary dynamically. This limits existing cooperative adaptive cruise control (CACC) strategies as most of them assume a fixed IFT. To address this problem, a CACC scheme is introduced that considers a dynamic information flow topology (CACC-DIFT) for CAV platoons. An adaptive proportional-derivative (PD) controller under a two-predecessor-following IFT is proposed to attenuate the negative effects when communication failures occur. The parameters of the PD controller are determined to ensure the string stability of the platoon. Furthermore, the proposed PD controller also factors the performance of individual vehicles. Hence, when communication failure occurs, the system will switch to a certain type of CACC instead of degenerating to adaptive cruise control, which improves the platoon control performance considerably. The effectiveness of the proposed CACC-DIFT is validated through numerical experiments based on Next Generation Simulation (NGSIM) field data. Simulation results indicate that the proposed CACC-DIFT design outperforms CACC based on a predetermined information flow topology.