BMW 528i 1996 E39 Ignition Problem

I've just bought the car (has done 83,000km) and everything is perfect
execept the issue i'm having with the ignition. In the morning when I go to
work it fires up with no problems, however as soon as the engine gets warm,
it takes up to 3-4 seconds to start it up again. Sometimes it kinda fires
up but shuts down - then the 2nd time as I said it takes up to 4 second to
fire up.... I took it to the mechanic and he replaced the crankshaft sensor
which reported the fault but it still hasn't fixed it. Does anybody had a
similar problem or any ideas what it might be? Much Appreciated.