Annie simply put loses a lot of her kill power in a long drawn out game, most all AP based heroes fall behind physical based ones. (such as Annie may toss tristana around like a second plushie doll but in a long game tristana can laugh at annie).
Annie is at her prime early to mid game and this is why is so vital for annie to get solo mid. I also recommend getting Mejais if your doing well as it can propel your AP quickly to give you a monster mid game and allow room for more flexibility in your item build.
If you do well enough mid game, you should hopefully gain a large enough level, gold and mejai stack advantage to make a very quick endgame, in that case Annie is still a monster to be feared.
If however you can not end the game quickly and endgame drags on, Annie will fall behind to physical carries and ultra beefed up tanks. It can suck but Annie is lucky in that her stuns are still useful and so she still brings a whole lot to a team fight.
If I find that the game is going long and I plainly can not keep up with the other teams carries and tanks (assuming I am not my teams carry eek!) then I even begin to turn my item build into a tanking one so I can be durable stun bot for my team over glass cannon.