Are they? If some of them are sensitive, that's because the DC/DC converter inside doesnot compansate that sag and the microprocessor needs a certain voltage level. However that is not the case in every PLC. I mean this is not a general rule.
Most PLC's run their program in RAM. If the DC voltage from the PLC power supply fades out it will corrupt the memory. It is therefor
necessary to detect a drop in AC Line voltage and signal the PLC to stop running to prevent this from happening. Hope this answers your
question.
James Johnson