A new component was reported in the X-ray counterpart to the binary neutron-star merger and gravitational wave event GW170817, exceeding the afterglow emission from an off-axis structured jet. The afterglow emission from the kilonova/macronova ejecta may explain the X-ray excess but exceeds the radio observations if the spectrum is the same. We propose a fallback accretion model that a part of ejecta from the neutron star merger falls back and forms a disk around the central compact object. In the super-Eddington accretion phase, the X-ray luminosity stays near the Eddington limit of a few solar masses and the radio is weak, as observed. This will be followed by a power law decay. The duration of the constant luminosity phase conveys the initial fallback timescale $t_0$ in the past. The current multi-year duration requires $t_0 > 3$--$30$ sec, suggesting that the disk wind rather than the dynamical ejecta falls back after the jet launch. Future observations in the next decades will probe the timescale of $t_0 sim 10$--$10^4$ sec, around the time of extended emission in short gamma-ray bursts. The fallback accretion has not been halted by the $r$-process heating, implying that fission is weak on the year scale. We predict that the X-ray counterpart will disappear in a few decades due to the $r$-process halting or the depletion of fallback matter.
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