iPhone keeps dropping USB connection

My iPhone 3GS keeps getting disconnected from the USB port of my Mac Mini. I have tried restarting the phone and the mini as well as various other tricks found on Google.

When the phone is connected to the USB port, it gives the "charging" beep and sometimes it immediately disconnects while at other times it loses the connection after a minute or two. I have tried changing ports, using a different cable and connecting it to my PC, everything yielded the same fruitless result :(

Could anyone help with this please?

Thanks

IMZ