With the known vulnerability of neural networks to distribution shift, maintaining reliability in learning-enabled cyber-physical systems poses a salient challenge. In response, many existing methods adopt a detect and abstain methodology, aiming to detect distribution shift at inference time so that the learning-enabled component can abstain from decision-making. This approach, however, has limited use in real-world applications. We instead propose a monitor and recover paradigm as a promising direction for future research. This philosophy emphasizes 1) robust safety monitoring instead of distribution shift detection and 2) distribution shift recovery instead of abstention. We discuss two examples from our recent work.