"Down like a prom queen" is a phrase often used to denote the rapid and complete failure of any given person, group of people, or thing concerning a particular task or set of events. It is an extension of the oft-used term "go down", however it is something of a pun as well, as it refers to the lesser-used connotation of this term. This other definition, of course, refers to oral sex, and thus the phrase hinges on the quite crude stereotype of a high school prom queen whore who might be quite willing and ready to showcase her talents.
Although this phrase is often used as a taunt, be it in a joking or threatening manner ("Just wait until next week, your team is gonna go down like a prom queen!"), it is also used when concerning a general breakdown under severe circumstances ("Our website got linked on Slashdot and proceeded to go down like a prom queen.").
Other variants of this phrase exist, which play on similar stereotypes, such as "down like a cheerleader on prom night".