The recently discovered SrFeO2 prepared by a soft chemical route from a precursor SrFeO3 has the 'infinite layer" (IL) structure with an unprecedented FeO4 square-planar coordination. We show that the IL structure has significant solubility to yield Sr(1-x)Ca(x)Feo(2) (0 <= x <= 1) and is thermally stable (at least as high as 1000 K for SrFeO2). These results demonstrate that the IL structure, once it is formed at low temperatures, is surprisingly robust owing to the extremely covalent nature of the Fe-O bond, thereby opening a door to chemical tuning of properties and to possible high-temperature applications.