This exact issue just happened to me last week.
Pretty sure it's the Flash Unit cause I have tried other 600ex-RT on the camera and all works fine. Have tried the problem 600ex-rt on another camera and same issue (can't get to ETTL mode).
I can set the 600ex-rt to ETTL but as soon as I 1/2 press the shutter on the camera, it will change back to TTL. If I use it the 600ex-rt in remove mode (slave), then I can use it in ETTL mode.
May have to send the 600ex-rt in for repair