I have the optional voltage regulators installed. The 5V regulator is this one, rated to 30V:
http://uk.farnell.com/texas-instruments/lp2950-50lpre3/ic-v-reg-ldo-5-0v-to-92-3-2950/dp/1262363
And I am definitely feeding the voltage regulator, not the 5V line directly. I made that mistake on a previous board and fed 9V from a battery directly to the 5V line by misunderstanding the power system.
As I said above the board itself all works fine. It is just the INA219 that seems to have stopped working.
-Matt