I’ve only come across this ‘not charging’ issue on a OnePlus One phone so far, and the fix which works for me is a bit… peculiar.
Sometimes when you plug in the charging cable it looks for a moment like the phone starts charging, only to stop after a matter of seconds and switch to status ‘Not charging’ on the status screen.
Should this happen you should try to insert the USB connector very slowly into the phone, until the phone sees it and starts charging. Then you push the USB connector further in, as deep as you’d normally insert it.
Don’t ask me why or how this works though…
[hat tip: vchristaras]