This paper presents extensions of control barrier function (CBF) theory to systems with disturbances wherein a controller only receives measurements infrequently and operates open-loop between measurements, while still satisfying state constraints. The paper considers both impulsive and continuous actuators, and models the actuators, measurements, disturbances, and timing constraints as a hybrid dynamical system. We then design an open-loop observer that bounds the worst-case uncertainty between measurements. We develop definitions of CBFs for both actuation cases, and corresponding conditions on the control input to guarantee satisfaction of the state constraints. We apply these conditions to simulations of a satellite rendezvous in an elliptical orbit and autonomous orbit stationkeeping.