Large low-Earth orbit (LEO) satellite networks are being built to provide low-latency broadband Internet access to a global subscriber base. In addition to network transmissions, researchers have proposed embedding compute resources in satellites to support LEO edge computing. To make software systems ready for the LEO edge, they need to be adapted for its unique execution environment, e.g., to support handovers in face of satellite mobility. So far, research around LEO edge software systems has focused on the predictable behavior of satellite networks, such as orbital movements. Additionally, we must also consider failure patterns, e.g., effects of radiation on compute hardware in space. In this paper, we present a taxonomy of failures that may occur in LEO edge computing and how they could affect software systems. From there, we derive considerations for LEO edge software systems and lay out avenues for future work.