FPGAs are being used in large numbers within cloud computing to provide high-performance, low-power alternatives to more traditional computing structures. While FPGAs provide a number of important benefits to cloud computing environments, they are susceptible to radiation-induced soft errors, which can lead to silent data corruption or system instability. Although soft errors within a single FPGA occur infrequently, soft errors in large-scale FPGAs systems can occur at a relatively high rate. This paper investigates the failure rate of several FPGA applications running within an FPGA cloud computing node by performing fault injection experiments to determine the susceptibility of these applications to soft-errors. The results from these experiments suggest that silent data corruption will occur every few hours within a 100,000 node FPGA system and that such a system can only maintain high-levels of reliability for short periods of operation. These results suggest that soft-error detection and mitigation techniques may be needed in large-scale FPGA systems.