Cooperative awareness and its evolution to collective perception is one of the key building blocks of the Intelligent Transportation Systems (ITS). Cooperative awareness is achieved by continuously exchanging update messages between neighboring nodes (vehicles, pedestrians, infrastructure) interacting on the road. A promising technology designed to support cooperative awareness is 5G NR-V2X, which enables sidelink communications through its Mode 2 operation mode. In Mode 2, vehicles can use Semi-Persistent Scheduling (SPS) to autonomously select and reserve resources to transmit successive messages. While the general performance of SPS has been studied recently, the impact of the persistence on the freshness of update messages has not been investigated. In this paper, we aim to answer the following question: is persistence beneficial in terms of the average Age of Information (AoI) metric? To this end, we define a simplified model of the SPS that lends itself to analytical evaluation and optimization. Comparison with simulations shows that the model is quite accurate and robust. Using this model, we obtain evidence for the existence of an optimal persistence level, which is not apparent when looking at other performance metrics, such as throughput or simply Peak AoI (PAoI). The optimal persistence probability emerges when looking at the system through the lens of average AoI.