  Recent follow-up observations of the binary neutron star (NS) merging event
GW170817/SGRB 170817A reveal that its X-ray/optical/radio emissions are
brightening continuously up to $\sim 100$ days post-merger. This late-time
brightening is unexpected from the kilonova model or the off-axis top-hat jet
model for gamma-ray burst afterglows. In this paper, by assuming that the
merger remnant is a long-lived NS, we propose that the interaction between an
electron-positron-pair ($e^+e^-$) wind from the central NS and the jet could
produce a long-lived reverse shock, from which a new emission component would
rise and can interpret current observations well. The magnetic-field-induced
ellipticity of the NS is taken to be $4 \times 10^{-5}$ in our modeling, so
that the braking of the NS is mainly through the gravitational wave (GW)
radiation rather than the magnetic dipole radiation, and the emission
luminosity at early times would not exceed the observational limits. In our
scenario, since the peak time of the brightening is roughly equal to the
spin-down time scale of the NS, the accurate peak time may help constrain the
ellipticity of the remnant NS. We suggest that radio polarization observations
of the brightening would help to distinguish our scenario from other scenarios.
Future observations on a large sample of short gamma-ray burst afterglows or
detections of GW signals from merger remnants would test our scenario.
