This paper studies assortative matching in a non‐stationary search‐and‐matching model with non‐transferable payoffs. Non‐stationarity entails that the number and characteristics of agents searching evolve endogenously over time. Assortative matching can fail in non‐stationary environments under conditions for which Morgan (1995) and Smith (2006) show that it occurs in the steady state. This is due to the risk of worsening match prospects inherent to non‐stationary environments. The main contribution of this paper is to derive the weakest sufficient conditions on payoffs for which matching is assortative. In addition to known steady state conditions, more desirable individuals must be less risk‐averse in the sense of Arrow–Pratt.