Accompanying code: https://github.com/EPFL-LCN/pub-seeholzer2018The ability to transiently memorize positions in the visual field is crucial for behavior. Models and experiments have shown that such memories can be maintained in networks of cortical neurons with a continuum of possible activity states, that reflects the continuum of positions in the environment. However, the accuracy of positions stored in such networks will degrade over time due to the noisiness of neuronal signaling and imperfections of the biological substrate. Previous work in simplified models has shown that synaptic short-term plasticity could stabilize this degradation by dynamically up- or down-regulating the strength of synaptic connections, thereby “pinning down” memorized positions. Here, we present a general theory that accurately predicts the extent of this “pinning down” by short-term plasticity in a broad class of biologically plausible network models, thereby untangling the interplay of varying biological sources of noise with short-term plasticity. Importantly, our work provides a novel theoretical link from the microscopic substrate of working memory—neurons and synaptic connections—to observable behavioral correlates, for example the susceptibility to distracting stimuli.