Stability has long been regarded as an important characteristic of many natural and social processes. In regards to scientific collaborations, we define stability to reflect the consistent investment of a certain amount of effort into a relationship. In this paper, we provide an explicit definition of a new indicator of stability, based on the year-to-year publication output of collaborations. We conduct a large-scale analysis of stability among collaborations between authors publishing in the field of computer science. Collaborations with medium–high degree of stability tend to occur most frequently, and on average, have the highest average scientific impact. We explore other “circumstances”, reflecting the composition of collaborators, that may interact with the relationship between stability and impact, and show that (1) Transdisciplinary collaborations with low stability leads to high impact publications; (2) Stable collaboration with the collaborative author pairs showing greater difference in scientific age or career impact can produce high impact publications; and (3) Highly-cited collaborators whose publications have a large number of co-authors do not keep stable collaborations. We also demonstrate how our indicator for stability can be used alongside other similar indicators, such as persistence, to better understand the nature of scientific collaboration, and outline a new taxonomy of collaborations.