Current Anonymous Communication Systems (ACS) lack fault tolerance and thus risk becoming unavailable when failures occur, forcing users offline or to less private messengers. In this work, we evaluate end-to-end message transmission latencies and resource demands of state-of-the-art mixnet Vuvuzela and CPIR system Pung under different network failure scenarios on an ACS test bed across four continents. We compare Vuvuzela and Pung to proof-of-concept mixnet FTMix that we equip with simple fault tolerance measures. Our analysis shows that FTMix maintains the smallest divergence of end-to-end latencies under failures from their respective baseline among all three ACS, while also achieving a balanced resource consumption trade-off. Thus, we consider fault tolerance effective in ensuring service availability and a crucial design principle for future ACS proposals.