We don't have a clue what car you have. Which means that we have no clue what the capabilities of the USB port and the radio in your car happen to be.
The USB port in my car works great with an iPod. Haven't tried it with my iPhone since I also have Bluetooth in the car and that is even better.
I'm not too clear from your description exactly what's happening. If the connection is going in and out, you should get another cable and/or verify it's making a good tight connection in the USB port. It could be a short some place else in the cabling of the car also.
The best two places to look for help are going to be your vehicle's owners manual and find a forum for your vehicle. At least there you'll find others with your car and your radio.