In this work, we study the long-term mechanical strength under static load - i.e. static fatigue performance or resistance to subcritical crack growth - of ceramic thick-film circuits, namely how the static fatigue of the substrate is affected by the presence of thick-film compositions on the surface subjected to tensile stress. Three substrate materials were compared: standard 96% alumina (Al2O3) and two grades of high-strength zirconia-toughened alumina (ZTA). The tested thick-film compositions included Ag- and Au-based conductors, a multilayer dielectric, resistors, and an overglaze, alone or in combination. The tests were carried out by applying a nominally constant load on cantilevers, at room temperature and in nominally 100% humidity, with stress data extracted according to log-normal and Weibull statistics. In the blank state, both ZTA grades exhibit higher short-term strength than 96% Al2O3, as well as much higher resistance to static fatigue. However, many thick-film compositions are found to degrade the static fatigue performance, with higher-strength ZTA being in general more affected. This implies that thick-film materials used in circuits under high mechanical stress, such as force and pressure sensors and devices operating in harsh environments, must be carefully chosen and placed in order to ensure reliable long-term operation.