I am using the LT3751 as low noise regulator configuration. Unfortunately its high voltage drops to zero on power-up immediately after reaching to the predefined value.
What could be the reasons for this behavior?
Are the boards you are using your own design?
I suggest that:
Try to interchange the IC of the working board with the board to verify if the IC is the problem or not.
This might be a board issue and not a design one(datasheet reference schematic) since you've said that some of them are working correctly.