Silver nanowire transparent electrodes have received much attention as a replacement for indium tin oxide, particularly in organic solar cells. In this paper, we show that when silver nanowire electrodes conduct current at levels encountered in organic solar cells, the electrodes can fail in as little as 2 days. Electrode failure is caused by Joule heating which causes the nanowires to breakup and thus create an electrical discontinuity in the nanowire film. More heat is created, and thus failure occurs sooner, in more resistive electrodes and at higher current densities. Suggestions to improve the stability of silver nanowire electrodes are given.