On my campus, you go to the office to see whether you have a bid card or not. If you didnt get one then there is no explanation, but they tell you not to let it deter you and that there is always winter rush which is more comfortable and less competitive.
There are tooo many reason for why a girl may not get asked back, and if your campus has the computerized system, its even more difficult to explain, because even though a sorority may have loved you. The computer will match the first 42 girls who wanted that sorority (and 42 is the quota for XYZ), if you're 43 you're kinda SOL. Truthfully youd probably have to give a reason to over 400 girls depending on the school as to why the didnt get a bid.