Under the “About” section I see it was revived for the 2014-2015 academic year “after a brief hiatus”. Then there is this disclaimer at the end:

Although this organization has members who are University of Virginia students and may have University employees associated or engaged in its activities and affairs, the organization is not apart of or an agency of the University. It is a separate and independent organization which is responsible for and manages its own activities and affairs. The University does not direct, supervise or control the organization and is not responsible for the organization’s contracts, acts or omissions.

For the name, the “history” section has this.

UVa student Ernest M. Stires suggested the title Corks & Curls, and a contest was held for the best rationalization of the name. Leander Fogg (of the Medical Class) won. Fogg explained that cork described an unprepared student who was called upon in class but who remained silent, like a corked-up bottle. In contrast, curl referred to a student who performed well in class and who, when patted on his head by his professor, “curleth his tail for delight thereat.” One might cork an examination but put a curl on a quiz.

(His head –> the school was all male at that time.)

It seems that was about 1888, when the yearbook group was first organized.

The editors of Volume I said that they placed Corks in front of Curls for modesty’s sake. “The title thus chosen was a happy one,” they suggested. “Unique, indigenous, esoteric, it is full of meaning for the elect, while at the same time it piques the curiosity of the uninitiated.”

What the history page does not give is information about the reason(s) the yearbook was on its hiatus.

Edited (yowza!!!!) to add:

Apparently the yearbook went on hiatus in 2008 for financial reasons.

http://www.cavalierdaily.com/article/2015/10/uva-corks-and-curls-2014-15-edition