I have a 6.6 volt input for Vin and only 1 ma of current available limited by a constant current diode. My supply has 2 outputs 2.7 and 1.8 using 2 of the TPS6212s. I power up fine but if I raise the input power slowly or jiggle power on I can get the Vout on either or both supplies to "stall" at 1.3Vdc. The supplies were drawing too much current, probably because it was trying to switchmode the current at too low of input voltage. I had the Enable pin tied to Vin. I now took my enable pin to a voltage divider dividing Vin to about 2 volts when Vin is 6V and tied that to the enable on the TPS62122s (sharing the divider to both parts.) works perfect now. I am respectful of the spec that enable needs 50uA of current and sized the resistors to accommodate the 50uA. Do you see any downside of doing that? I basically have the enable pin sitting at 2 volts in normal operation with my 6.6 volt input. Any better ideas?