I'm having the exact same issue, has anyone else experienced this or have a fix for it, I'm using an HP Elitedesk Mini with HP DisplayPort adapter and have tried a G1 and G3 model, I have also tried the following:
Tried 2 different chipset model desktops (HP Elitedesk G1 and G3)
2 different DisplayPort adapters - generic + genuine HP
2 different HDMI cables
Firmware upgrade on the Activpanel
Promethean driver upgrade
Intel Graphics driver upgrade
Desktop PC BIOS upgrade
Promethean Support call - the only suggestion they had was to try it on a computer with an HDMI port, due to the location of the computer this will be very difficult, a standard sized desktop won't fit.
As Jon said above, physically switching the DisplayPort cables (Activpanel and monitor) kicks it back to life but it is very annoying for the teacher.
Any suggestions would be gratefully received