Yar, on my mkv (and my fiancee's 2004 polo) the heated mirrors are operated by the switch on the door being in the correct position - completely independant of the rear screen. On the mk5, if the computer decides the battery voltage is getting low it will automatically start powering down non essential items, with the first item being the heated mirrors.* Presumably the same is true of the mk6.
*Source: T_T