If I were a writer and the my fans appreciated my work, I would work hard to maintain that appreciation.
Which could mean not sending in the book to the publisher until the author is satisfied that all the problems have been worked out and it represents the author's best writing. Is it the author who labors on for years who is not keeping faith with their readers or the one who slaps together an inferior piece of work every nine months or less just to meet their deadlines? (Note, some people
can be incredibly prolific and incredibly good both at the same time. Not everyone though. And even those who can ... maybe not forever.)
I'd also like to point out two things.
1) Creativity is not something that can invariably be turned on and off at will. When we're old enough to be experienced and young and healthy enough to be writing at the height of our powers, this may be possible. When that is not the case, then putting pressure on in some of the ways that have been suggested in some of the posts above could actually be counterproductive.
2) An author might start writing a series at a comparatively favorable time in their life. Their health is OK, and whatever their chronological age may be, mind and body are not doing badly. Optimistically, they believe that this is how things will continue long enough for them to finish the series. Why wouldn't it? Sure, things may go wrong here and there, and they'll be a year or two late with a book sometimes, but overall they expect they'll be fine, even with all the other commitments they've made. After all, they've never had more than minor problems keeping up before. And as for growing older, well, some people are still sharp as tacks into their eighties and nineties. Then ... life happens. Three or four or five books in everything has changed. The characters and the plot are not cooperating. The brain is beginning to struggle just getting words out. (The writer goes to his or her doctor,
hoping they can find something wrong, something that can be fixed. "Nope" says the doctor, "that's perfectly normal for someone your age." "But people much older than I am are still as productive as they were in their twenties and thirties." "Yes, they're the lucky ones. Sorry. Try to take better care of yourself; that will help some.") The time between books stretches out from one year, to five years, to ten, and consequently age is catching up with them faster and faster.
Trust me, at this stage there is
no threat a publisher can make,
no action they can take, that will get the book written in a timely manner and to an acceptable standard. And, yes, probably the writer should have been more realistic years ago in their expectations of how fast they'd get the series written. Too late to do anything about that now.