At what point do iPads stop displaying "not charging" when connected to power?

The iPad manual (page 136) and other Apple documentation (see bottom) are not very specific in this regard meaning...

• ...they do not state specific minimum currents required for charging.

• ...they only distinguish between:

  • charging while the iPad is awake (USB hubs with 1100 mA; newer Macs/displays)
  • charging while the iPad is in sleep mode (USB hubs with 500 mA; standard USB/old Macs)

Low-battery image or “Not Charging” message appears

or

• When charging, make sure you’re using the 10W USB power adapter that came with iPad or the USB port on a recent Mac. The fastest way to charge is to use the power adapter.
• For faster charging, turn iPad off.
• iPad may not charge when connected to the USB port on an older Mac, a PC, a keyboard, or to a USB hub.
• If your Mac or PC doesn’t provide enough power to charge iPad, a Not Charging message appears in the status bar. To charge iPad, disconnect it from your computer and connect it to a power outlet using the included Dock Connector to USB Cable and 10W USB power adapter.

Also see the following documents:

• iPad: Charging the battery
• Batteries: iPad