Take this reply with a pinch of salt.
At the moment (and for the test I made), I found a solution launching the (Control Panel) -> Troubleshoot -> (under Find and Fix other problems) -> Hardware and Devices.
Windows has found some problems and has fixed it.
From that moment on, the pen has not given me any more trouble and it seems to work even after long standby times, and even if I turn off and on again the bluetooth voluntarily.