I suspect that the problem is in the fuel return circuit.
I had the same problem in my BMW 320i.
There is a spring loaded piston on the fuel distributor and there are o rings in there that get worn. This allows fuel pressure to bleed off and there is no pressure when you hit the key.
It doesn't affect cold start as the cold start injector circuit provides fuel.
Here's a link to a very good book.
http://www.amazon.com/exec/obidos/tg/detail/-/0837603005/qid=1129734271/sr=8-1/ref=pd_bbs_1/002-3995347-5796015?v=glance&s=books&n=507846
Good luck.
Mark