I following the page Bluetooth Low Energy for developing in Android 4.3 for Bluetooth Low Energy .
I already can turn on the Bluetooth
My workaround to the problem was to delay the reconnection:
private void connectGatt(final String address) {
new Timer().schedule(new TimerTask() {
@Override
public void run() {
bluetoothGatt = bluetoothManager.getAdapter().getRemoteDevice(address).connectGatt(context, true, bluetoothGattCallback);
}
}, 500);
}