The problem of interest is the detection of transient signals in additive white Gaussian noise (AWGN) in the presence of missing signal observations (samples). Specifically, a fusion center aims at detecting the presence of transient signals by collecting measurements from individual sensors through erasure channels. Under the assumption that the fusion center can control the sampling procedure through a feedback channel, a strategy is proposed to adapt the sampling rate in response to sample missing with the goal of achieving accurate and timely decisions with the minimum communication cost measured by sampling rate. The proposed strategy is flexible in that it can be configured to suit different performance requirements. Compared with fixed-rate sampling, the proposed strategy achieves better tradeoff between Quality of Detection (QoD) and communication cost through dynamic adaptation.