When a failure or upset occurring in a controller computer induces a task failure durable for a substantial period, system dynamics apparently deviates from its desirable sample paths, and loses its stability in an extreme case for the period to exceed the hard deadline in a real-time control system. In the paper, we propose an algorithm to combine the deadlines of all elementary tasks (derived formerly by our work) executed in several operation modes with multi-sampling periods. This results in computing the hard deadline of the entire system through modifying task-state equations to capture the effects of task failures and inter-correlations among tasks.