The regulator was not removed yet, no, the behaviour was with my unmodified sensor. I have actually now started looking at an alternative power setup so that i can use this mod at 3.3v and drop the requiment for it to run from 4.5v (which was based on running it upregulated from 3 AAs with an attiny85 woken up from sleep mode - which worked well and consumed ~0.1mA overall). Back to the drawing board :)

I am trying to figure out if running this modification from 3 AAs at 4.5V will work (it is for a setup with a attiny85 that I want to run from 4.5 down to 3.3v - it currently works well from 5 down to 4.5 with exactly the erratic behaviour explained above from about 4.4v and down). When looking at the datasheet for the BIS0001 then it seems like it will fine? What am I missing? :)