We report surprising new observations, both in Lancaster and in Moscow, of pulsed NMR in He-3 below 200 muK at 0 bar. At these low temperatures an extremely long induction decay signal of up to 25 s duration is observed. This signal develops from a state of the He-3 with coherent spin precession, formed spontaneously after an NMR excitation pulse in the presence of an inhomogeneous magnetic field and differs from the well-known state with homogeneous precession (HPD) observed at higher temperatures. We believe that this signal indicates a persistent coherent magnetic state which appears when the normal component dissipation becomes negligible at the very low temperatures.