This technical note considers remote state estimation subject to limited sensor-estimator communication rate. We propose a stochastic online sensor scheduler for remote state estimation with time-out condition. The decision rule under which the sensor sends data is based on its measurements and a finite-state holding time between the present and the most recent sensor-to-estimator communication instance. This decision process is formulated as an optimization problem, relaxed and solved using generalized geometric programming optimization techniques with a low computational complexity. Moreover, the proposed scheduler is easy to execute, and provides a guaranteed performance which is shown to outperform the optimal offline scheduler. Numerical examples are provided to illustrate the proposed scheduler.