Not only the children but also the parents need to believe in Santa.
Parents buy presents for their children, because they don't have faith in Santa bringing them. Suppose there is a Clause which says that if the parents don't believe in Santa, the children don't get any presents from him. There isn't anywhere in the stories (as far as I know) which says that children should suffer for their parents' lack of faith, but it's possible.
We can disprove this though with the help of orphaned children in warzones. They have no parents or generally any care-givers to take on the parental role, but they don't get presents.
So forget this one, and move onto another more interesting possibility.
Santa's definition of naughty and nice is not the same as ours.
Suppose Santa has a completely different moral code to us. He's a different species with advanced technology, after all - who can tell how he thinks? Human ethics have evolved with improved knowledge, longer lifespans, and rejection of corrupting mythologies and oppressive customs. This is good for society as a whole; but it may not meet Santa's requirements.
Suppose Santa is a trickster god. In that case he might choose to reward children who are comprehensively disruptive to those around them. Since society trains children to not behave this way, very few children will meet his requirements. This seems unlikely, because in the environment of general scarcity which existed before the last few decades, society didn't have enough spare capacity to deal with awkward kids.
More chillingly, what if his red suit reflects something else though? Midwinter sacrificial rites were a major part of many European traditions. Usually these only involved animals and not human sacrifice, but even animal sacrifice is no longer part of our culture. So perhaps children are no longer getting presents from Santa because they aren't killing animals in his name. This would tie in rather nicely with everything we know about the season, everything we know about European winter traditions, and with changes to social norms.
Interestingly, this hypothesis is also impossible to falsify. Even if a child killed an animal, a formal sacrifice requires some ceremony around it otherwise it doesn't count. Any ceremonies attached to Santa's sacrifice have long since been lost, and there is no way to recreate it because we wouldn't even know where to start. (We would also probably fall foul of animal protection organisations!)
I think this gives us the answer. Not only does it fit all the available facts and all the history, but it also gives us a reason why we cannot ever get back to Santa bringing presents for children.
And like all good Christmas stories, it is completely unprovable...