Getting dropped??

Coming from someone who knows a little bit more about how the logistics of recruitment works, it is very rare that someone is dropped from every house after round 1. In general (at any round), it is very rare that a girl is released from recruitment by every chapter on campus. More often than not, PNMs who do not end up with a bid choose to withdraw from recruitment because they aren't happy with their schedule - dropped from their top house(s), too few invites back, etc.
However, I'll be honest and say that it IS fairly common to see girls with very small/short schedules as early as round 2.

BUT please don't worry. The vast majority of PNMs get a bid. And if this year doesn't work out, you can always express interest in doing COB or you can rush again next year.
So take some deep breaths, have fun, and utilize your Rho Gam. I know it sucks starting college (or going into a new school year) with all this going on, but no matter what happens you'll be ok. Your Greek experience does not have to define your TCU experience if it makes you unhappy!

TL;DR - not likely to be dropped by all chapters, but could have a small invite schedule as early as round 2. But I promise you will be ok no matter what