We investigate the stability of utility-maximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing the number of active flows. When the rate region is convex, the stability region is known to coincide with the rate region, independently of the considered utility function. We show that for non-convex rate regions, the choice of the utility function is crucial to ensure maximum stability. The results are illustrated on the simple case of a wireless network consisting of two interacting base stations.