High current devices like the heated rear window can partially work if a connector gets contaminated, though more common on cars 30 years ago. Normally unplugging and plugging the connector a number of times + WD40 would fix it. Also could just be a bad earth depending on how its wired (e.g. like when you see cars with the wrong rear lights on when they brake...).
I am also interested in this. On Saturday my rear demist (A4 B8 Avant MY2010) stopped working altogether. I just did a VCDS scan and got:
02983 Connection between impedance converter 1 and window 011 - Open Circuit.
So I'm thinking that there's probably a connector which does both window heat and antenna.
I'll let you know if I make any more progress - planning to have a look this afternoon.
OK. The connection to the heating elements is at the top edge of the screen, slightly right of centre. You can prise back the interior trim with your hands or a flat plastic tool starting from the centre, and work outwards. That allows a good look at the solder connections. You could also check that the element isn't damaged between the solder joint and the rest of the window.
There are two connectors going into the long narrow box close to the soldered joints - anyone know what this is?
The coaxial one on the right can be removed by lifting the clip on it with a flat blade; the other one on the left with three wires pulls out towards you. I suppose these could be prime candidates for a dodgy connection.
There's a fuse (40A) and a relay for the window heat in the boot, on the right hand side behind the removable trim. I haven't worked out exactly which these are yet.
I take it that the inside of the screen is very clean...when i havent cleaned mine for a while it too takes a long time to demist