Do note that the spec has current limits that are pretty low at 7-8V. If you connect 2 Li-Ion batteries in series, they're able to provide several Amps of current, which exceeds the maximum specified in the charger spec. This is likely why you get "Not charging" message.

Battery low warning comes at 3.5V on internal battery, there are atleast 2 layers of sofware shutdown, with the first one happening shortly after battery low, and the second (backup?) shuts down the device at 3.2V..