I have a long standing issue with my 1st generation iPhone. It is unlocked (the original iPhone has never been formally supplied in my country) but I'm pretty sure that the problem is not associated with that.

What happens is that it stops charging. It will be on the charger with about half charge showing. It recognises that it is on the charger (wall charger or Mac usb via powered usb hub - makes no difference), but the charge levels drops down as the hours go past, eventually into the red, and finally it powers itself off.

It will then sometimes respond to power being connected or disconnected with the battery icon showing either the slightest sliver of red, or no red at all, and the little power bolt. Sometimes it will be completely black-screen unresponsive.

If left on the charger, it will eventually charge up again. This can happen within an hour or so, but once it took 3 days before it started charging. Sometimes the whole thing repeats immediately (within hours) after a successful re-charge. Sometimes I get several weeks of good behaviour before it misbehaves again.

I have tried putting it in recovery mode, and re-setting up from scratch.

Any other ideas?

I saw something resembling what you are describing on one iPhone. In that case the battery would sometimes get really warm. Not too hot to touch, but not particularly comfortable to hold. It turned out a third party app was getting hung running in background and continually polling the internet. I honestly don't remember the app, but it was isolated by removing the apps and systematically adding them back until the problem recurred.

Already tried that - one time I used recovery mode to re-build from scratch, I left it with only the standard apps. Problem happened again a couple of weeks later.

The odd thing to me is the irregularity of its occurrence.