Basically, It all depends on each magazines.
Shonen Jump is the most extreme example of the Japanese manga industry but is probably the most "transparent" in their decision making. (I'm going to talk about JUMP only, since it's the most transparent)
Before we speak about cancellations, here's how a newcomer gets serialized:
- Authors release a one-shot, they put it in one issue, and wait for the votes to come in. They usually do this with 2 or 3 new one shots.
From Issue #37/38 2013 (Double week issue), to issue #41 2013, Jump released 3 new one shots. (Ana no Mujina, Mochizuki, Tokudou!!)
But the number of "new series" are usually dependent on the number of canceled series. (From the same issue span, 1 series got canceled, which means normally only one would be serialized, but it's not strange if they didn't serialized any new one shots.
-For Cancellations, the criteria for getting cancelled in JUMP is simple, getting bad popularity rankings, regardless of the contents. Getting stuck on the 5 lowest for too long = the higher the possibility of cancellation.
But to make things easier for newcomers, they will get 7 free chapters from the start before they get "ranked", also getting a color page/center color/lead color means they are not "included" in the popularity rankings on that issue (another precious freebie).
The latest canceled manga "Smoky B.B" started on #26 ended on #41, Mutou Black started on #25 and ended on #36. After their first 7 chapters, both new series kept dwindling on the lower rankings.
-There's only one author that has a very special exception in Jump, which is the author of Hunter X Hunter, Togashi Yoshihiro.
-Authors can also end their mangas on their own, but this act is not well supported by the "Brass" because JUMP wants a long running series.
Besides JUMP, other manga magazines aren't that transparent on their decision making and mostly seems lenient seeing that there are series running for more than a decade. The longest running series that isn't from JUMP, is "Detective Conan" (Shonen Sunday), with 19 years of content.
Fairy Tail is also in Shonen Sunday, along with Hayate no Gotoku, Zettai Karen Children. It was also home to Air Gear, Inuyasha and Ranma 1/2
There are a lot of other manga magazines.
http://en.wikipedia.org/wiki/List_of_manga_magazines
Discussions about contents from Shonen JUMP
http://weeklyjump.livejournal.com/
About demographic trends, you need to work or have a close friend in those companies to get such information. But each magazine has their own target demographic, Shonen Jump and Sunday with Shonens (Male, Elementary Age to 15 years old). Young Jump, Young Animal, and Young Ace with Seinens. (Male, Age 18 to 30). And there's Shoujo and Josei the gender opposites.