For a steady-state mode interaction problem with symmetry Golubitsky, Stewart and Schaeffer (1988 Singularities and Groups in Bifurcation Theory vol II (New York: Springer) ch XIX) prove that there are parameter values for which a Hopf bifurcation occurs along a mixed-mode branch. The author has proved that it is always so in mode interaction problems with symmetry (Castro S B S D 1995 Mode interactions with symmetry Dyn. Stability Syst. 10 13 - 31). In this work, we are concerned with what happens to the limit cycle arising from this Hopf bifurcation. We find that, for certain parameter values, it vanishes through a homoclinic connection. To prove this, we use Melnikov theory since the equations under study are a perturbation of Hamiltonian equations. This completes the bifurcation diagrams in Golubitsky et al (above).