  We consider the dynamical evolution of two planets orbiting in the vicinity
of a first order mean motion reso- nance while simultaneously undergoing
eccentricity damping and convergent migration. Following Goldreich &
Schlichting (2014), we include a coupling between the dissipative semimajor
axis evolution and the damping of the eccentricities. In agreement with past
studies, we find that this coupling can lead to overstability of the resonance
and that for a certain range of parameters capture into resonance is only
temporary. Using a more general model, we show that whether overstable motion
can occur depends in a characteristic way on the mass ratio between the two
planets as well as their relative eccentricity damping timescales. Moreover, we
show that even when escape from resonance does occur, the timescale for escape
is long enough such at any given time a pair of planets is more likely to be
found in a resonance rather than migrating between them. Thus, we argue that
overstability of resonances cannot singlehandedly reconcile convergent
migration with the observed lack of Kepler planet pairs found near resonances.
However, it is possible that overstable motion in combination with other
effects such as large scale orbital instability could produce the observed
period ratio distribution.
