Speaking as an author and an applicant.

This is mostly my opinion, and I'm sure some of you will disagree, but again, an opinion. 

1) Your character isn't a fit to the story.

Applyfic will most likely invovlve an ensemble of characters fit in a certain theme. Authors would pick those that naturally fit better to the theme, leaving certain others out. 

Solution: Try to imagine that character directly into the story. Imagine them as a chosen one. What would they be?

2) There's a huge competition.

When there are a huge number of applicants against the settled number or plotlines, there's most likely a higher number of good applicants. Naturally, this makes things hard for the author, and a lot don't get chosen.

Solution: Try solution #1. If not, select another story that has less applicants (more love to them!) or plotlines. Win-win solution, is it not?

3) Again, competition.

Not just how the characters ended up in general, but the whole application. Characters that has flaws and issues that could be worked on usually looks more interesting and easier to develop. Those with more abundant information to them also helps the author a lot in writing. They also painted a lot about the character.

Aesthetics actually plays a pretty big role nowadays (and has been too), as much as denied it is. If it's not, then you wouldn't see a 'themed' layout frequently. Not all authors demand flowery words or perfect grammar either, but (in my opinion), applicants that had better writing had increased chances than those who aren't as proficient/prolific. Mostly because it does deliver better, the author gets a good grasp of character.

Solution: Decided a 'theme' to your character. What makes your character stands out a lot? What makes your character the one that deserves to be? After that, make your whole app with that focus.

4) Authors.

I... don't know. Some authors had made it clear that adding 'plus points' to your character would possibly make your character more likeable, but even authors have biases that is not known to the rest (author's knowledge of such biases does not matter). Characters that have brownie points may actually not get chosen, while those that lacked it may even be. 

It's unknown really. The 'additional' points aren't the only type of bias out there, but I'm afraid that's enough to exemplify. 

Doesn't necessarily means that these points are the worst, it's not exactly a bad idea to begin with. They are the one who created the applyfic, so they have freedom to make what they want. So are the applicants. Whether they wanted to add such things is not for anyone else to decide.

Solution: Ask the author? There's no clear solution except if you talk to them, or something.

5) Your characters have lack something to them.

People who applied so many times would probably know more about the substance that makes a character, but even first-timers do so too. Sometimes they don't get chosen because they just aren't what is wanted. They could have been a good fit, they fit what the author wants, but it's not simply there. The author just takes someone else for any given reason.

Solution: Try not to pin the blame on anyone, because except for special occasions, chosen apps cannot be reversed. Try to accept that fact and move on. 

How about you guys? What makes you think some characters don't get chosen?