As a general rule however, good quality coils are designed with a “hysteresis” of flux that will either pull in OR drop out a coil, it is very very difficult for it to flutter in a zone in which it does both. The typical values are 70% drop-out, 80% pull-in. So on a 120V coil that is already pulled in, it will not drop out until the voltage drops below 84V, but will not pull in again until the voltage rises again to 96V. This is done specifically to avoid this very situation and those values are baked into NEMA specifications.
If the LOAD on the coil powered device (ie a contactor) is large enough to AFFECT the voltage drop because the service is under sized, that’s where you can get into trouble. Let’s say you have a 200HP Motor fed by a 200kVA transformer. It might be enough to start and run it, but if the utility side drops too much, the coil drops out. That sheds the 200HP motor and the transformer recovers, raising the voltage to where the coil picks up again and pulls in the starter. That of course causes the voltage drop again and the coil let’s go again, repeat to destruction. I just used that one large motor to illustrate the point, it could also be 10 x 20 HP motors or 20 x 10 HP motors or 100 x 2HP motors; any total load that is too large for the service.
In order for this to take place, you MUST have a “2 wire control circuit”, meaning whatever is turning the load on and off is maintaining that command. In this case you mentioned a “Pico”, which was a small Allen Bradley “smart relay” or micro-PLC. It’s likely powered by a 24VDC power supply, and that power supply likely has a very wide range of input voltage at which it maintains the 24VDC, meaning at less than 84V, it is staying active, so its output controlling the coil stays closed, allowing this to happen. The simple solution would be the aforementioned line monitoring relay that is fed into an input of the Pico so that if the voltage does drop, it drops out all of the outputs and goes through a restart sequence wherein they don’t all try to turn back on at the same time and start the drop out cycle again. If it’s just one or two loads you can also program in a “starts-per-hour” limit to ensure that the contactors don’t cycle on and off again fire than a couple of times without a significant rest period between them. This by the way is ALSO going to be harming your motors, so it’s a wise plan for more than just the contactor coils.