In the context of cell-free massive multi-input multi-output (CFmMIMO), zero-forcing precoding (ZFP) is superior in terms of spectral efficiency. However, it suffers from channel aging owing to fronthaul and processing delays. In this paper, we propose a robust scheme coined delay-tolerant zero-forcing precoding (DT-ZFP), which exploits deep learning-aided channel prediction to alleviate the effect of outdated channel state information (CSI). A predictor consisting of a bank of user-specific predictive modules is specifically designed for such a multi-user scenario. Leveraging the degree of freedom brought by the prediction horizon, the delivery of CSI and precoded data through a fronthaul network and the transmission of user data and pilots over an air interface can be parallelized. Therefore, DT-ZFP not only effectively combats channel aging but also avoids the inefficient Stop-and-Wait mechanism of the canonical ZFP in CFmMIMO.