The simple surface included in the attached file can’t be split by the pipe that was built from a projected curve onto the surface. For some reason Rhino will refuse to find intersection between the ball end cap of the pipe and the surface. I was able to split the surface by replacing the ball end cap with a true ball, but I thought that reporting this particular case may help improve Rhino in the future and reduce other cases like this.
Hi Bobi - bring the file tolerance down to .001 and it will work. It does seem like it ought to at .01 but passing through a singularity may cause extra complications. With a more arbirtrarily oriented sphere, it does work at .01.
RH-66822 SSX short through pole
-Pascal
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Hi Pascal, that worked and I know the trick with bumping the tolerance, though I would wish that the file tolerance of 0,01 mm could handle it properly, because the ball diameter of 5 mm is big enough to not make that issue. 
If you remember, I notified you multiple times during the past few years about that strange behaviour of Rhino when it comes to splitting. A quick forum search brings a topic I created specifically for that issue: