It's hard to make an applyfic. 

Even harder to get people interested.

Worst, finish the thing.

There's a lot of reasons why they don't really finish, me being there, but it could always be chalked up with some things.

1) Authors are also people in real life.

So they get busy. Not all authors are still in highschool, and not all of them are still in their teens. Some have reached adulthood and college age, so they have more responsibilities. Their stuff is still more important than the applyfic they have, so don't get surprised that they don't really reach completion. 

Solution: Probably divide the responsibility from applyfics and jobs are the best thing to do.

2) They really don't know where to go with the story.

The characters are established, but the plot isn't exactly clear. Often found in purely idol group applyfics and slice-of-life fics, which comprises the majority of the applyfics. Often writer's block would even attack a good premise, and the author could barely update for months.

Solution: 1) Try put in a big outline on how the story goes, and where to end it. Plotting the story doesn't really work when someone gets burst of ideas that may change the outline, but it would be really good at any given times.

2) Write the ending first if you're stuck, and started writing from the back. Example:

a) idol group X debuted.

b) ?

c) they won on their frst year

So they won, but how did they won? Could be "The company used chart manipulators" or something close to that. It'll make the story have things to deal with next time.

3) They don't gain enough support.

Not enough applicants. Seriously, it pains the author, even if they know making a character is hard, but getting ignored isn't exactly easy. Many authors that tried picking up their long-hiatus stories would find out that many of their applicants had been inactive, and they get discouraged because they have to write a story that just doesn't have much support. Even just as the story starts, some applicants barely commented. Reminder, these authors write your characters, so the only one who most likely would give those responses would be the applicants themselves.

4) They just don't have anymore interest.

Combination of factors (lack of support, a lack of a storyline, issues, etc.) would accelerate this factor up. What used to be the new, shiny fic would become boring. Also, commitment issues with applyfics happened. Some people just lost interest.

5) Others.

Factors that are rarely a reason, but still happens. 

6) Seriously, it's hard.

Authors have to promote their stuff so applicants could apply. Then, if the story even moves, they have to establish the characters of each applicants fairly and equally (which is quite hard). Gets worse with bigger ensembles, but that's the way to get more comments (and that's why there's so many applyfics that wanted large numbers of applicants). And the characters must be of what the applicants have made (trust me, your author is looking at your application as they write your characters in a chapter). It's a pain to fit so many in once, that most people just gets tired.

Solution: establish a commitment with the fic. The applicants have made their own sacrifices in hopes to see the story going, even with the fact that it might not even continue. 

Honestly, I've been on both the side of the applicants and the author who almost never completed anything. My main factor has always been support, but I wonder what's other people's factor?