I started to have the dreaded Bluetooth/Wi-Fi malfunctioning message, not after a firmware update (mine was already at 4.0 when I bought it used), but during filming.
I had a Bluetooth RC, and it was working well until it didn't. I thought it was the battery in the RC, but then I went to the Sony A1 menu and realized the Bluetooth was OFF. Tried to switch to ON, and that's when I got the malfunctioning message.
What's interesting is that the WiFi still seems to work OK.
I was using Bluetooth all the time for GPS tagging... and sometimes for remote control with the phone.
Not sure what can be done, the camera is out of warranty anyway, and the repair may cost too much.