Just saw this post and I've had the same issue while using Energizer lithium’s and phantom. Seems like they have addressed this in the ‘new’ DR-40X machine, as quoted in the firmware notes:
V1.02 fixes
- When operating on AA batteries, if phantom power was turned on, the unit would shut down on rare occasions.
This has been fixed.
As a workaround for my deck, I plug in mics, switch phantom off, power up the deck and put the machine in internal mic mode, switch on phantom, then put the mode back to external (mic) input. Works every time.