Gonorrhea is also commonly known by the slang term "the clap" - suggested etymology from the Old French word "clapier", meaning "brothel". (Another suggested source for the term is from the notorious 18th century brothel keeper known as "Mother Clap", though perhaps her name itself was derived from the slang term). It could also refer to the painful sting in the male urethra, which feels like the sting of a clap when infected with this disease.

But the online etymological dictionary says:

"gonorrhea," 1587, of unknown origin, perhaps from M.E. claper, from O.Fr. clapoire, originally "rabbit burrow" but given a slang extension to "brothel." Originally also a v., "to infect with clap."

And, Take Our Word for It says:

For those of you wondering where the clap, another term for gonorrhea, came from, no one knows for certain. It dates from the late 16th century, though the verb to clap "to infect with gonorrhea" surfaced a bit earlier. One source suggests that the verb derives from "to clap one's hands on," but that does seem a bit tenuous. A better possible explanation is that it comes from Old French clapoir "venereal bubo". So what the heck is a bubo? It's a swelling or boil, especially in the groin. Eeew!

I guess the short answer is, "nobody knows."