dropped by every house

Some will drop out of the rush process on their own. I know it has to happen once in a while but I think it's very uncommon. Age is a factor, but if you really click with the girls in the house, it won't matter as much. For example, if you're a junior and they like you a lot, you'll likely get a bid over a freshman that they feel meh about.

There is a quota. Last year the top houses took 3-4 juniors I believe

People are so unnecessarily negative about juniors rushing for some reason. Don't listen to them. Last year, a higher percentage of juniors that rushed ended up pledging than sophomores and freshmen that rushed (the ones who didn't pledge either removed themselves from rush [more common] or didn't get a bid). This year fewer juniors will be rushing because a huge amount of sophomores who would have chosen to rush junior year joined Alpha Gamma Delta instead.

Juniors and seniors are judged in a different category than sophomores and freshmen to protect against discrimination. In addition, houses can invited back more juniors/seniors because they are not counted in the "cap." Some houses may use GPA to get rid of older girls (high school gpa vs. college gpa are very different, but for the most part I would say you have a better shot as a junior than as a sophomore.