In complex real-time systems, specific functionality is generally implemented by a cause-effect chain, which is a sequence of multi-rate real-time tasks with data dependency. One of the critical prerequisites for the correct operation of such systems is that the external event is timely captured by the first task of the corresponding chain, propagated to the last task and generates a response during a predefined time interval. Most of existing work assumes the external event keeps continuously valid and focuses on when the response will be generated. However, in actual scenarios, the external event may become invalid shortly after its occurrence and there will never be a response to it. This paper considers such external events with finite validity intervals and proposes techniques to analyze the minimum validity interval of an external event to guarantee the existence of a corresponding response. Experiments with both a randomly generated workload and a case study are conducted to evaluate and verify the proposed techniques.