Hi. Check the fuses first for the wiper pump for the rear hatch...it COULD be that simple. BUT at that age, it is the pump burned out.
I have a 2006 Aveo HatchBack, it is the same car, and i have the same problem and have had it for a year now. It is such a pain, it was so nice to be able to clean the hatch with the push of the wiper stalk. I see you are in the UK,...KALOS is the AVEO name over there. Just to let you know, the pump you are looking for is attached to the windshield washer tank in the engine compartment.
There are 2 separate pumps there, one for the front, and one for the hatchback. It has burned out. The pump itself is fairly cheap, its on EBay and its cheap there, so from some other sellers, it is probably even cheaper. BUT to replace it, is a bit difficult. You have to remove the inner fender well plastic cover on the front drivers side. To expose the wiper fluid tank, and see the pumps attached to it, take out the correct one, put in a new one, hope there is no 'junk' in your line going to the back window, and the fluid will go to it again. It looks like a easy job to fix, but I personally dont know how to remove the wheel well plastic, and not break it.
I know it is attached with plastic 'screws/plugs', and I don't know how to remove them, and get the wheel well cover out of the way. But that is where your pump is located. I hope that helps. Go on EBay and look for a windshield washer pump, for a 2006 Chevy Aveo HB, and you'll see it, maybe get the GM code number, if you want to search online for it. But put in Chevy Aveo,..Kalos is not well known on EBay.
It is the SAME CAR, and you'll see what pump you need. Then maybe on You Tube, or on here, someone can tell you how to replace it. No one has told me, so I don't know. And the dealer wants WAY to much to do it. I assume the wiper is still working? As long as it is still working, then it is JUST the pump burned out on the tank. Let me know if you get it fixed, how much it cost you, if you do it, and how it goes. Good luck.