On a generic enough level, they fail because they:
Aren't any better than non-moderates at fixing problems
Are worse than non-moderates at selling the promise that they will fix problems
Often, are part of "establishment" that people are dis-satisfied with due to problems - they either get blamed for the problems or for not having had fixed them.
Another factor is that "moderate" is a squishy vague term. One can argue that some of the new populist parties/leaders are true moderates and that the establishment parties went off "moderate" space some time ago and that is why they are being replaced as a choice. If you try to push the Overton window hard enough, you risk falling out of Overton window.