I have a 2011 Liberty w/ the Sky Slider canvas roof. I work in the auto body industry, I personally wouldn't recommend taking it through a automated car wash. Read the signs at your local car wash it says that they are NOT responsible for damage to your vehicle. I have seen factory installed roof racks get broke or bent (my grandmothers Rav4 rack was broken). Most car washes in my area won't allow convertibles though and with the canvas top, it should be treated the same way. So if you are willing to risk it go ahead it could be fine, but personally I wouldn't. (FYI if damaged it could cost over $1,000 to fix) Its not that Jeep has a bad product it's that automated car wash brushes get caught of protruding edges such as gaps at the edges of the canvas.
thats just a general good idea to not use touch car washes. all the dirt and grime from every vehicle before is still on the brushes rubbing up on your paint. besides the fact they break stuff they will make 1,000,000 little scratches all over your jeep