If the supply of MAX17651 or LDOs in general drops below the output voltage, the bypass cap of the LDO will discharge via the body diode of the power FET. This can severely impact the behavior of the LDO, worst case even create a device damage as there is no current limiting resistor in the path.
To prevent mal function and device damage, use a Schottky diode between the LDO output and the LDO supply that is strong enough to handle the reverse current (cathode at LDO supply). This will protect against device damage and avoid the body diode of the integrated FET to turn on.