The permanence of eye movements as a biometric modality remains largely unexplored in the literature. The present study addresses this limitation by evaluating a novel exponentially-dilated convolutional neural network for eye movement authentication using a recently proposed longitudinal dataset known as GazeBase. The network is trained using multi-similarity loss, which directly enables the enrollment and authentication of out-of-sample users. In addition, this study includes an exhaustive analysis of the effects of evaluating on various tasks and downsampling from 1000 Hz to several lower sampling rates. Our results reveal that reasonable authentication accuracy may be achieved even during both a low-cognitive-load task and at low sampling rates. Moreover, we find that eye movements are quite resilient against template aging after as long as 3 years.