  We investigate the secular evolution of the orbital semi-major axis and
eccentricity due to mass transfer in eccentric binaries, allowing for both mass
and angular momentum loss from the system. Adopting a delta function mass
transfer rate at the periastron of the binary orbit, we find that, depending on
the initial binary properties at the onset of mass transfer, the orbital
semi-major axis and eccentricity can either increase or decrease at a rate
linearly proportional to the magnitude of the mass transfer rate at periastron.
The range of initial binary mass ratios and eccentricities that leads to
increasing orbital semi-major axes and eccentricities broadens with increasing
degrees of mass loss from the system and narrows with increasing orbital
angular momentum loss from the binary. Comparison with tidal evolution
timescales shows that the usual assumption of rapid circularization at the
onset of mass transfer in eccentric binaries is not justified, irrespective of
the degree of systemic mass and angular momentum loss. This work extends our
previous results for conservative mass transfer in eccentric binaries and can
be incorporated into binary evolution and population synthesis codes to model
non-conservative mass transfer in eccentric binaries.
