A colloidal ring driven in the direction normal to the ring offers valuable insights into unstable many-particle dynamics in overdamped active systems, compared with systems in an underdamped regime. This model is one of the rare cases where a many-body problem with long-range correlations is reduced in the continuum limit to a two-body nearest-neighbor problem. The dynamics is governed by a competition between the driving forces, which act to inflate the ring, and hydrodynamic interactions, which tend to deflate it. As a proof of concept, we examine a perfectly circular ring and derive the critical drive for which the ring changes from deflation to inflation. We check two models for the two-dimensional hydrodynamic interactions: one that corresponds to motion within a membrane, and the other to a ring confined between two walls. The analytical results in the continuum limit are in excellent agreement with the numerical ones for a ring of discrete particles.