For real-time systems, most of the analysis involves efficient or exact schedulability checking. While this is important, analysis is often based on the assumption that the task parameters such as execution requirements and inter-arrival times between jobs are known exactly. In most cases, however, only a worst-case estimate of these quantities is available at the time of analysis. It is therefore imperative that schedulability analysis hold for better parameter values (Sustainable Analysis). On the other hand, if the task or system parameters turn out to be worse off, then the analysis should tolerate some deterioration (Robust Analysis). Robust analysis is especially important, because the implication of task schedulability is often weakened in the presence of optimizations that are performed on its code, or dynamic system parameters. In this work, we define and address sustainability and robustness questions for analysis of embedded real-time software that is modeled by conditional real-time tasks. Specifically, we show that, while the analysis is sustainable for changes in the task such as lower job execution times and increased relative deadlines, it is not the case for code changes such as job splitting and reordering. We discuss the impact of these results in the context of common compiler optimizations, and then develop robust schedulability techniques for operations where the original analysis is not sustainable.