Thin, supported inorganic mesoporous membranes are used for the removal of salts, small molecules (PFAS, dyes, and polyanions) and particulate species (oil droplets) from aqueous sources with high flux and selectivity. Nanofiltration membranes can reject simple salts with 80–100% selectivity through a space charge mechanism. Rejection by size selectivity can be near 100% since the membranes can have a very narrow size distribution. Mesoporous membranes have received particular interest due to their (potential) stability under operational conditions and during defouling operations. More recently, membranes with extreme stability became interesting with the advent of in situ fouling mitigation by means of ultrasound emitted from within the membrane structure. For this reason, we explored the stability of available and new membranes with accelerated lifetime tests in aqueous solutions at various temperatures and pH values. Of the available ceria, titania, and magnetite membranes, none were actually stable under all test conditions. In earlier work, it was established that mesoporous alumina membranes have very poor stability. A new nanofiltration membrane was made of cubic zirconia membranes that exhibited near-perfect stability. A new ultrafiltration membrane was made of amorphous silica that was fully stable in ultrapure water at 80 °C. This work provides details of membrane synthesis, stability characterization and data and their interpretation.