We report on the magnetic-field-driven persistent ferromagnetic (FM) state in antiferromagnetic (AF) manganite Pr1-xCaxMnO3, where x=0.4 and 0.375. At low temperatures the magnetic field-induced ferromagnetism (FIFM) persists even at B=0 and is quenched to a fractional value of the total number of spins. This incomplete ferromagnetism decreases with increasing temperature and disappears at T-m=10-20 K. T-m depends on the hole concentration "x" and increases as x-->0.3. We interpret this as the incomplete relaxation from FM toward AF spin orientation, resulting in the canted antiferromagnetism (CAF). This is in contrast to the "virgin" (zero-field cooled) magnetic ground state where no ferromagnetic component could be detected. Due to the strong competition between FM and AF orders, three successive AF transitions are detected. The low-temperature transition at T-3= 27 K has a strong influence on FIFM, resulting in the minimum magnetic field required to trigger the FIFM state. Furthermore, the T-3=27 K transition results in a pronounced anomaly in the temperature variation in magnetization. We comment on this property in the light of a similar finding in the phase-separated La0.21Pr0.42Ca3/8MnO3 which was interpreted as the strain-glass transition.