I actually had my 6FL cable work flawlessly for months before this same thing happened. I bought a replacement OEM cable and it did exactly as you described; 20-30 good seconds and then it cuts out.
Drives me nuts because if I want to play from my phone I have to plug in to the auxiliary jacks (can't select songs through drive this way) and if I want to use the idrive to song select I have to load a flash drive with music (can't alter contents without reconnecting to a computer).
Issue first pronounced itself on my 3G. Now I have an iPhone 4 with the new iOS and have the same issue.