In the 1970s, the trend started for movies to continue a story until you had numerous parts. Such as Star Wars, Part IV, V, VI and then Part I, II, III. And soon we will have another Rocky movie. Is that number 8 or 9?
Then in the 1980s, I started to see books doing the same. Sometimes you would have the same hero and heroine, but more often you would have stories from the previous secondary characters' POV.
Now, myself, I like the secondary character stories, though I always had problems with having the hero and heroine in more than one book. I don’t know why, but when I read their story and come to the end, I want to think they are happy and no more problems will come their way. So give me the secondary characters, and leave the original hero and heroine alone.
And from what I’ve seen in readers’ websites, they love the secondary character stories, too. They want to know everybody in every book is happy. And it doesn’t necessarily have to be the "good" ones. Even the villains, if they live, need a resolution and be saved from themselves.
The only problems I have with some secondary character books are when the previous hero and heroine show up and almost take over the book. Or the author feels compelled to tell you about the other story and the role the now hero or heroine played. Usually too much unnecessary back story.
Do you have problems with continuing books? Secondary characters? Or series?