I had a similar situation just a few weeks back. Something to the effect that the rear window has to be "reset" to remember where the full shut position is. First see if your rear window defrost is also not working, to confirm the symptom is not just the rear window by itself.
Check your rear window wiper and rear defroster-it is my guess those are out of commission as well. Check the fuses, but if those are fine then use the inside rear window control -or the key at the rear hatch to raise the window all the way to the top.
It is my guess you will see it move just a hair of an inch, or by putting it all the way down and then all the way up you will "reset" the memory.
If your defrost and wiper are working fine then check the window at both switch locations to narrow down the trouble.
Let us know what you find out.... I think this is a fairly common problem that a lot of us never really knew about it until it happened to us personally.