The only explanations I can think of are:
When you power on, a transient is putting the MAX31856 info fault mode. Does the green Fault LED turn on?
The 3.3V power rail is coming up very slowly and this is causing the MAx31856 chip to be initialised before it is ready.
If you power up the Duet with the thermocouple connected, and then send a M305 P2 X151 T"K" command manually (you should not need to repeat the heater name), does it work then? If so then a fix might be to use a G4 delay command in config.g. You could try executing that command twice, with a delay in between.