Angel Beats! - Visual Novel Details & Ongoing Speculation

[Yerian]

I really want that to be a thing.

You’re in luck. Straight from Dengeki G

Angel Beats! & Charlotte news from Visualstyle and Dengeki G's magazines

Completing a character’s route doesn’t necessarily mean that they will disappear. But at the very least, by the end of the 6th game they’ll have all disappeared eventually.
After finishing a route, you are looped back to the beginning.
If a character does disappear, then they will remain absent from the game in future loops.