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Due to their ability to provide a shape memory effect at elevated temperatures, high-temperature shape memory alloys (HT-SMAs) came into focus of academia and industry in the last decades. Ternary and quaternary Ni–Ti-based HT-SMAs have been in focus of a large number of studies so far. Ti–Ta HT-SMAs feature attractive shape memory properties along with significantly higher ductility and lower costs for alloying elements compared to conventional Ni–Ti-based HT-SMAs, which qualifies them as promising candidate alloys for high-temperature applications. Unfortunately, precipitation of undesired phases, e.g., the ω-phase, leads to significant functional degradation upon cyclic loading in binary Ti–Ta. Therefore, additions of ternary elements, such as Al, which suppress the ω-phase formation, are important. In the present study, the influence of different heating–cooling rates on the cyclic functional properties of a Ti–20Ta–5Al HT-SMA is investigated. Transmission electron microscopy as well as in situ synchrotron analysis revealed unexpected degradation mechanisms in the novel alloy studied. Elementary microstructural mechanisms leading to a degradation of the functional properties were identified, and the ramifications with respect to application of Ti–Ta–Al HT-SMAs are discussed.