I don't know about the rest of Europe, but in Denmark, universities get a part of their funding based on the number of graduates. So the university has an incentive to help student actually graduate instead of kicking them out. That may or may not matter to the bureaucrat responding to an appeal - but I'd certainly not just assume that "I'm close to graduation, just let me do this one more exam attempt" isn't a good enough reason for them to let you try.
Ah, well in the Czech Republic universities get funding based on the number of currently enrolled students, not graduates. Some places will therefore accept 1000 into a CS program, only to have <100 people actually graduate.
As for the appeal - these usually aren't successful, even my thesis advisor said that he probably wouldn't go out of his way to talk to the analysis course examiner etc. etc.