Temporal constraint networks are embedded in many planning and scheduling problems. In dynamic problems, a fundamental challenge is to decide whether such a network can be executed as uncertainty is revealed over time. Very little work in this domain has been done in the probabilistic context. In this paper, we propose a Temporal Constraint Network (TCN) model where durations of uncertain activities are represented by random variables. We wish to know whether such a network is robust controllable, i.e. can be executed dynamically within a given failure probability, and if so, how one might find a feasible schedule as the uncertainty variables are revealed dynamically. We present a computationally tractable and efficient approach to solve this problem. Experimentally, we study how the failure probability is affected by various network properties of the underlying TCN, and the relationship of failure rates between robust and weak controllability.