The quality of the communication channel between human-robot teammates critically influences the team's ability to perform a task safely and effectively. In this paper, we present a nine person pilot study that investigates the effects of different degradations of that communication channel, and within three shared-autonomy paradigms that differ according to how and at what level control is partitioned between the human and the autonomy. Accordingly, the rate and granularity of the human input differs for each shared-autonomy paradigm. We refer to each paradigm according to the input expected from the user, namely high-level, mid-level and low-level control paradigms. We find three primary insights. First, interruptions in the signal transmission (dropped signals) decrease safety and performance in modes where continuous and high-bandwidth inputs from the human are expected. Second, decreased transmission frequency offers a trade-off between safety and performance for low-level and mid-level control paradigms. Lastly, noise alters the safety of high-level input since the user is not continually correcting the signal. These insights inform us when to shift autonomy levels depending on the quality of the communication channel, which can vary with time. Knowing the ground truth of how the signal was degraded, we evaluate a recurrent neural network's ability to classify whether the communication channel is experiencing lowered transmission frequency, dropped signals or noise, and we find an accuracy of 90% when operating with low-level commands. Combined with the key insights, our results indicate that a framework to dynamically allocate autonomy between the user and robot could improve overall performance.