You can manage a series where each story is an individual, stand alone work with its own plot and everything. Or where there's an overarching story. But random incidents, with each conflict spawned by an arc, but characters treating them as episodes, don't work as well. As Aristotle warned
Unity of plot does not, as some persons think, consist in the Unity of the hero. For infinitely various are the incidents in one man's life which cannot be reduced to unity; and so, too, there are many actions of one man out of which we cannot make one action. Hence, the error, as it appears, of all poets who have composed a Heracleid, a Theseid, or other poems of the kind. They imagine that as Heracles was one man, the story of Heracles must also be a unity.
And it applies to other things, too. For instance, all the incidents occurring in a fight against some Dark Lord in an epic fantasy.
What weakens these series the most, I think, is that the problem in each book is neither foreshadowed in the earlier books nor causing the characters to kick themselves for not realizing it would happen. It's all very well for the wandering swordsman to feature in a story where he fights a necromancer, and another where he fights the dragon; wandering is not something that connects a plot. (Those authors who want connection will probably have to build a bildungsroman.)