Take the case of an infinion smart switch, whose datasheet describes very well the reasoning. Say in the case of a smart switch (smart mosfet) you tell it to turn on and power a large load, if the voltage is dragged below the cutoff voltage it shuts down, having turned the output off the input voltage rises again, so it goes again and again trigger the low voltage cut off, the result is that the chip oscillates and overheats, because it keeps restarting the overheat protection can't function properly and it burns out. To prevent this they demand you put a decent amount of capacitance close by. You may have a similar problem but it sounds like they have tried to slow things down with a large hysteresis.