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We report on the fast Nova Sgr 2016 N.4 being surprisingly trapped in a long-lasting and bright plateau (Delta I >= 10 mag above quiescence) six years past the nova eruption. Very few other novae experience a similar occurrence. We carried out an intensive observing campaign collecting daily BVRI photometry and monthly high-resolution optical spectroscopy, and observed the nova in ultraviolet and X-rays with Swift satellite at five distinct epochs. The bolometric luminosity radiated during the plateau is ~4200 Lsun (scaled to the distance of the Galactic Bulge), corresponding to stable nuclear burning on a 0.6 Msun white dwarf. A stable wind is blown off at FWZI~1600 km/s, with episodic reinforcement of a faster FWZI~3400 km/s mass loss, probably oriented along the polar directions. The collision of these winds could power the emission detected in X-rays. The burning shell has an outer radius of ~25 Rsun at which the effective temperature is ~7600 K, values similar to those of a F0 II/Ib bright giant. The Delta m < 1 mag variability displayed during the plateau is best described as chaotic, with the irregular appearance of quasi-periodic oscillations with a periodicity of 15-17 days. A limited amount of dust (~3x10^(-11) Msun) continuously condenses at T(dust)~1200 K in the outflowing wind, radiating L(dust)~52 Lsun.