Studies have shown that the morphologies of galaxies are substantially transformed following coalescence after a merger, but post-mergers are notoriously difficult to identify, especially in imaging that is shallow or low-resolution. We train convolutional neural networks (CNNs) to identify simulated post-merger galaxies in a range of image qualities, modelled after five real surveys: the Sloan Digital Sky Survey (SDSS), the Dark Energy Camera Legacy Survey (DECaLS), the Canada-France Imaging Survey (CFIS), the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP), and the Legacy Survey of Space and Time (LSST). Holding constant all variables other than imaging quality, we present the performance of the CNNs on reserved test set data for each image quality. The success of CNNs on a given dataset is found to be sensitive to both imaging depth and resolution. We find that post-merger recovery generally increases with depth, but that limiting 5σ point-source depths in excess of ∼25 mag, similar to what is achieved in CFIS, are only marginally beneficial. Finally, we present the results of a cross-survey inference experiment, and find that CNNs trained on a given image quality can sometimes be applied to different imaging data to good effect. The work presented here therefore represents a useful reference for the application of CNNs for merger searches in both current and future imaging surveys.