The amount of time the pelts stay on the boards varies with the temperature and moisture. Basically, they stay on until they're dry. I know guys who board them for only a day before they're ready to come off, especially the "non-fatty" pelts like fox and muskrats. Coons, yotes, and beavers are much greasier and usually take longer, but if you have a good dry heat and fan to circulate the air, they'll dry quickly as well.
"Knowing when to shoot and when to wait is one sign of maturity in a bowhunter. Be patient and pick your aim point carefully." ~ Randy Ulmer
"I suppose it's the way of hunters. We are very odd fellows." ~ Peter Hathaway Capstick