This is crazy, mine is acting the same way - works once in a while then goes into the reading mode and ends with an error. Jeep told me that they are working on the problem with Apple.
Saw this at:
Additional service issues, tips and information
Apple iPad not compatible with UConnect
The Apple iPad is not compatible with Uconnect when connected to the vehicle’s USB port or ipod control cable located in the glove box or center console. The iPad will display the following message: “This device is not supported by the iPad”. UConnect system may display “Reading” and / or “Error” on the radio display.
Bluetooth Streaming Audio from iPad plays with no issue. However, seek up and seek down buttons on the radio are not supported by the iPad. Seek up and seek down operation can be exercised using the iPad itself.
Apple IPhone4 - Audio issues playing audio files
Customers may complain that while playing audio files from apple iPhone4, the sound will drop out or fail to play. Chrysler and Apple Inc. are jointly investigating this issue. Timing for a resolution from Apple and Chrysler is TBD.
The following solution should be suggested to customers in the interim:
Step 1: Turn the vehicle off
Step 2: Turn the iPhone4 off and on.
Step 3: Turn the vehicle on, and wait 30 seconds
Step 4: Connect the iPhone4 to vehicle's USB port (in glove box or center console) using the USB cable that came with the iPhone4 (generally the cable is White in color). Make sure that customers are using their device via USB port located in glove box or in the center console and not via the USB port on the radio faceplate.
Step 5: Press "Media" button on the radio and use the system in iPod (USB) mode (and not in Bluetooth Streaming mode)
Also, advise customers to minimize use of seek up and seek down keys; and when they are used, try not to press them multiple consecutive times.