For a given channel instance and a fixed LDPC ensemble, a stability outage event is defined by the density evolution being unstable at the origin. The probability of such an event, referred to as Stability Outage Probability, is a useful lower bound for the word error rate. We formulate the stability outage probability for block fading channels and we introduce the stability diversity order. As a direct application, we show how the class of capacity-achieving ensembles on the erasure channel is bounded away from the outage limit on a block fading channel.