We present a novel, previously unreported phenomenon appearing in a thermal gas of nonlinear polar molecules excited by a single THz pulse. We find that the induced orientation lasts long after the excitation pulse is over. In the case of symmetric-top molecules, the time-averaged orientation remains indefinitely constant, whereas in the case of asymmetric-top molecules the orientation persists for a long time after the end of the pulse. We discuss the underlying mechanism, study its nonmonotonous temperature and amplitude dependencies, and show that there exist optimal parameters for maximal residual orientation. The persistent orientation implies a long-lasting macroscopic dipole moment, which may be probed by even harmonic generation and may enable deflection by inhomogeneous electrostatic fields.