XBox360 wireless gamepad doesn't reconnect after turning it off and on

Hello!

I have a wireless XBox360 gamepad (VID 0x045E PID 0x0719). And when using it via GameInput it initially works well, but after turning it off and on again (e.g. by unplugging the battery and plugging it back), it doesn't reconnect back and inputs are not updated. On GameInput interface it stays "Connected". Only physically reconnecting the wireless receiver helps it to be reconnected propery and start working again.
I am listening to device state using:

gameInput->RegisterDeviceCallback(nullptr, GameInputKindGamepad, GameInputDeviceAnyStatus, GameInputBlockingEnumeration, this, &deviceCallback, &token);

and in a loop I am reading the specific device using:
gameInput->GetNextReading(lastReading, GameInputKindGamepad, device, &reading);
with a fallback to
gameInput->GetCurrentReading(GameInputKindGamepad, device, &reading);
if GetNextReading fails.

Via xInput it reconnects fine when turning it off and on during gameplay.

Verified on GameInput v3.1.26100.6879 and v3.2.138

Please let me know if you need more details

Start by reproducing the reconnect sequence with the listed Xbox 360 gamepad and GameInput versions, using RegisterDeviceCallback, GetNextReading, and GetCurrentReading as described. Compare the behavior with XInput; done means the device reconnects and inputs update without physically reconnecting the wireless receiver.