A systematic distance-dependent measurement of the quasistatic tip-sample interactions reveals a hidden stochastic dissipative interaction of the atomic-scale contact in dynamic force microscopy. By comparison of experiment with detailed molecular dynamics simulations, we demonstrate that the infrequently observed hysteresis loops are attributed to the formation of atomic chains during tip retraction. These lead to a large magnitude of energy dissipation in a single cycle and dominate the average measured dissipation, while also leading to differences in the forces measured in static and dynamic force microscopy. This paper provides quantitative force measurements and insights into atomic-scale dissipation processes.