One of the primary uses are deep space probes. The stirling engine has exactly two moving parts and uses non contact seals. In theory the lifetime should be limited by the deformation of the piston at elevated temperatures. Still, you’re right. They certainly have to do a lot of reliability testing to be able to show that these stirling engines will last 10+ years before they use them in a mission. They have several stirling engines that have been running for multiple years in simulated conditions for just this purpose at NASA GRC.
Your point about moving parts is good, it is absolutely the place to look for possible failure. That said, it is also possible to build such things in a durable way. For example, at the science museum in London there was a display with a Stirling engine that over 75 years old and still works fine. I expect the challenge will be to keep the materials within the range of temperatures and pressures that do not cause structural change in the material.
Has that stirling engine had zero maintnence in the last 75 years? If so that is quite impressive and gives much more confidence that NASA can pull this off with the benefit of three quarters of a centruty of technological advancement.
