I have not found this information (max current draw), but I have read other testimonials saying that the onboard voltage regulator dies frequently as soon as you connect another device to the board, being totally unable to feed anything else that the board (without any other device connected to the board).
The specs say that the Vin input voltage should be [7 to 12V], I have reduced it to 9V but a few boards died, as said by other persons.
The main device connected to the boards were a LCD screen (via I2C), that draws 10mA (I have measured it this afternoon). There were also a Reed relays board, but asking only 10mA during 0.5 second, not often (there can be many seconds or minutes between two relays actions).
So today I have placed a small 5V power supply nearby the Mega Mini, in order to feed it with 5V, connected to the "5V" pin.
In a large part of the webistes, this "5V" pin is described as a "5V output", only a few of them have specs saying 'Input or output'.
This new small P.S. transforms my 12V source in 5V , via a 7805 equivalent. I have added a small basic dissipator to the 7805.
I have measured that the [Mega Mini+LCD screen] draw 80mA with this 5V power supply. This combination has worked continuously during 8 hours: the 7805 gets tepid (not cold but not very hot), so I believe that it should be reliable even enclosed in a small chassis.
I will make it working continuously tomorrow, but I believe that this should solve the issue.
I hope this will help other persons.