We should let the author, Stephenie Meyer, answer this question:
According to a post on her web site, she was planning a fifth book in the series, which she titled "Midnight Sun." However, before she had finished writing the manuscript, someone stole a copy and uploaded to the Internet. Here is what she says about the theft:
I did not want my readers to experience Midnight Sun before it was completed, edited and published. I think it is important for everybody to understand that what happened was a huge violation of my rights as an author, not to mention me as a human being.
So what are her plans for the manuscript? Here's what she says about that:
So where does this leave Midnight Sun? My first feeling was that there was no way to continue. Writing isn't like math; in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything. If I tried to write Midnight Sun now, in my current frame of mind, James would probably win and all the Cullens would die, which wouldn't dovetail too well with the original story. In any case, I feel too sad about what has happened to continue working on Midnight Sun, and so it is on hold indefinitely.
I'd rather my fans not read this version of Midnight Sun. It was only an incomplete draft; the writing is messy and flawed and full of mistakes. But how do I comment on this violation without driving more people to look for the illegal posting? It has taken me a while to decide how and if I could respond. But to end the confusion, I've decided to make the draft available here....This way, my readers don't have to feel they have to make a sacrifice to stay honest. I hope this fragment gives you further insight into Edward's head and adds a new dimension to the Twilight story. That's what inspired me to write it in the first place.
Visit her web site for the full story of what happened and the complete letter to her fans.
Few outside of Stephanie Meyer and the publishers would have a definitive answer to it. I think that a couple of things have to enter into the equation. The first would be if the series continues to be popular and such a commercially successful venture. If recent history has revealed anything, it would be that the more commercially profitable a series it is, the longer the life it has. There is little evidence to suggest that its popularity would wane. However, with its core audience, taste is fickle. If the audience becomes entranced with another work, Meyer's series might fade a bit. I would also suggest that the success of the film series would prolong any potential growth of the enterprise. Finally, there might be a chance that Meyer, herself, might seek to try her hand in another venue or with another work before churning out another one in the current series.
There have been 4 books in the Twilight series. Twilight, New Moon, Eclipse, and Breaking Dawn. I have heard a rumor of Meyer's finishing Midnight Sun which will be in Edward's point of view but we shall see.
Since this question was posted Stephanie Meyer has put Midnight Sun on the back burner. However, fans were rewarded with The Second Life of Bree Tanner. It came as a complete surprise to us all. The Second Life of Bree Tanner is the companion of Eclipse and features the newborn vampire that the Cullen's were going to take in but the Volturi decided to ultimately kill.