This paper addresses the problem of automatically detecting and quantifying performance degradation in remote mobile robots during task execution. A robot may encounter a variety of uncertainties and adversities during task execution, which can impair its ability to carry out tasks effectively and cause its performance to degrade. Such situations can be mitigated or averted by timely detection and intervention (e.g., by a remote human supervisor taking over control in teleoperation mode). Inspired by patient triaging systems in hospitals, we introduce the framework of "robot vitals" for estimating overall "robot health". A robot's vitals are a set of indicators that estimate the extent of performance degradation faced by a robot at a given point in time. Robot health is a metric that combines robot vitals into a single scalar value estimate of performance degradation. Experiments, both in simulation and on a real mobile robot, demonstrate that the proposed robot vitals and robot health can be used effectively to estimate robot performance degradation during runtime.