Yeah the problem is that AAA batteries just aren't very good. Alkalines are the worst of a bad bunch really.
Yes, the problem seems to be too much amp draw from power source that can not provide it. But still, what puzzels me is why the light just does not go dim or off, but to this very slow blinking in low mode. Like one blink per second. This driver should not have any blinking modes. No blinking modes accessible at least. But it still blinks. I didn't find any data sheet or other info which could explain it. Some kind of protective circuit might do that, I suppose. But if that's the reason, it's not very well set.
But it's just a setback. Not dead end. Or even better, this is an opportunity to maybe learn something. I will not give up. I will make a light that runs neutral R4 on the cheapest of the low quality AAA's one can find. I may have to reprogram the driver. I may even have to use another driver. But there will be a day when I will post a new thread titled "3xAAA alkaline powered neutral white L2i by HID45". You can count on that. Just don't hold your breath.