The answer is 'Yes, when there wasn't time to figure out how to deal with the surge'
An interesting point is that your board would shut down when *another* unit was swapped. That would point to loading the main power.
I assume you are using switching power supplies on your board. As Vin drops, Iin increases. In addition, have you simulated / measured the Switching currents vs. input step response? These can be an order of magnitude higher than the nominal load current during severe input or output steps (depending on the switcher).
To put this in perspective - when a redundant power supply is swapped, the power supplies will start to share (swapped in) or heavily load one supply (swapped out). In either case, you can expect a step on Vin. This can easily lead to high pulse currents for your internal switchers. Those high pulse currents don't have to last very long to trigger the shutdown feature of the controller you are using.
The solution in that case is to check the device you are using against switching currents during Vin steps, and perhaps change to one that has slightly slower Vout response in return for lower pulse currents. Changing the output inductor can help here, but if it's a voltage mode controller, you'll have to re-calculate the loop compensation, which is quite a hassle.
Of course, you could increase the capacitance on the inputs of the internal supplies, but that then loads the system giving larger inrush currents (although that can be dealt with using this controller).
So my hypothesis is a Vin step causing large impulse currents in your internal supplies that last long enough to trigger shutdown on the controller.
Cheers
PeteS