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 similar to 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 (SGRB) afterglows. In this Letter, 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 x 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, because the peak time of the brightening is roughly equal to the spin-down timescale 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.