This paper investigates whether low-order packet-loss statistics suffice to assess survival-time risk under bursty packet losses, i.e., the probability that no update succeeds for a prescribed number of consecutive slots. Conventional models, such as the Gilbert model, characterize packet losses using the loss rate and mean burst length, but channels sharing these statistics may exhibit substantially different failure risks. We characterize the Markov channels one order above a given low-order fit that share its statistics and analyze their risks under acknowledgment-based scheduling with transmission budgets. We show that, with dense transmission attempts, risk is primarily governed by loss persistence beyond the modeled memory, and the worst-case channel need not be the most persistent one. Under limited budgets, retry spacing makes loss relapse probabilities important and can reverse the risk ordering of compatible channels. Numerical and measurement results show that low-order models can substantially underestimate the risk, highlighting the need for scheduling-dependent channel statistics.

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