We determine the smallest instantaneous increase in the strength of an opposing windthat is necessary to permanently reverse the forward displacement flow that is drivenby a two-layer thermal stratification. With an interpretation in terms of the flow’s ener-getics, the results clarify why the ventilation of a confined space with a stably-stratifiedbuoyancy field is less susceptible to being permanently reversed by the wind than theventilation of a space with a uniform buoyancy field. For large opposing wind strengthswe derive analytical upper and lower bounds for the system’s marginal stability, which ex-hibit a good agreement with the exact solution, even for modest opposing wind strengths.The work extends a previous formulation of the problem (Lishman & Woods 2009,Build-ing and Env.44, pp. 666-673) by accounting for the transient dynamics and energeticsassociated with the homogenisation of the interior, which prove to play a significant rolein buffering temporal variations in the wind.