After proceed with a firmware update on JDY-08 to the HM-10 official one (following 1saac_k guides) and a lot of time unsuccessfully spent trying to send AT commands to the module, I've figured out that the following must be done:
System KEY function (PIO0):
Long press system KEY >=1000 ms.
After wake up module, you can send and receive AT commands.
(ref. http://eezone.co.uk/blog/wireless/hm-10-cc2541-4-0-ble-bluetooth-to-uart-transceiver-module.html)
According to 1saac_k (again) after the firmware update the System KEY pin on the JDY-08 board is mapped as the pin 09.
That way to send AT commands to the module through UART interface, the pin 09 (or the PIO0 on the HM-10) must be pulled down (GND) for at least 1 second after the board power on and after every bluetooth connection established.
Best,