No doubt your own diagnosis is correct as to shutdown caused by repeated inrush current. There's another factor caused by sudden removal of a load from the boost converter. Unless regulation is super-quick to reduce duty cycle, only a few cycles need occur to drive capacitor charge soaring to alarmingly high volt levels. It's easy to observe with an oscilloscope.
In any case consider making two stages of capacitive filtering, with resistor in between. The second capacitor varies widely as the load turns on and off. The first capacitor stays at more or less stable voltage, serving as a reservoir. Although the resistor wastes power (as heat), try adjusting values until your shutdown problem is cured, yet with acceptable power loss.
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