...
LTC4418 automatically controls the switches so start there
An inrush of current could trigger an UV fault (disconnecting source)
Voltages are out of their threshold values (11V - 15V) when they reach the IC (including conversion to the internal 1V threshold)
During switching, large inductive spikes are tripping OV thresholds repeatedly
Is there larger than 3V on the output during startup?
2x8.4uF on input and output which when switch closes, voltage will average across, which could be below the UV trip point
Use larger input CAP
UV threshold lowered? This would worsen the voltage averaging affect, allowing us to be below the other threshold if one was lower than the other (explains the one way effect)
Check resistor values and calculate changed UV and OV thresholds
Increase retry interval to attempt to avoid continual switching
...