VW Phaeton does not sporadically start (starter spins)

Hello everyone, I have a very annoying problem with my thick! It’s a VW Phaeton 3D year 06/2005 with the 3.0 TDI engine and automatic transmission. The problem is as follows, sporadically it doesn’t jump on. If the error is there there are no error messages or similar the starter turns off quite normally for about 2-3 seconds but then turns off on its own, even if I hold keys in starting position. I can’t reproduce the error myself, sometimes it’s not at all a few days. It was also for example already when I drove 30km then briefly refuel and see it doesn’t jump on. Sometimes it goes after the 10 times try sometimes but also after 1-2 hours again. I already tried it with both keys and a new power supply battery installed unfortunately without success. Can it be if the engine rotates normally at the roadblock lie? Has someone already had such a case? I hope you can help me with every help position.