We consider loop observables in gauged Wess-Zumino-Witten models, and study the action of renormalization group flows on them. In the WZW model based on a compact Lie group G, we analyze at the classical level how the space of renormalizable defects is reduced upon the imposition of global and affine symmetries. We identify families of loop observables which are invariant with respect to an affine symmetry corresponding to a subgroup H of G, and show that they descend to gauge-invariant defects in the gauged model based on G/H. We study the flows acting on these families perturbatively, and quantize the fixed points of the flows exactly. From their action on boundary states, we present a derivation of the "generalized Affleck-Ludwig rule", which describes a large class of boundary renormalization group flows in rational conformal field theories.