The task of failure prognosis requires the prediction of impending failures. This technical note formulates and studies the problem of distributed prognosis of discrete event systems, where the local prognosers exchange their observations for the sake of arriving at a prognostic decision. The observations are exchanged over communication channels that introduce bounded delays. A property of joint-prognosability is introduced to capture the condition under which any failure can be predicted by some local prognoser prior to its occurrence. We provide an algorithm to check the joint-prognosability property.