Fresh Rabbit Pelts are acquired by harvesting a Rabbit Carcass. They can then be cured by leaving them indoors for 3 days (in-game). Fresh Rabbit Pelts Decay at a rate of 6.667 Condition a day (Stalker difficulty) and will decay into Ruined status if not left to cure indoors. The current curing status can be checked by hovering your reticle over the item, where it will display a "X% Cured" progress. This increases until the item is 100% cured, where the item will automatically become fully cured, will change to a darker texture, and is ready for crafting use. Completely cured items never decay.
Rabbit Pelts are acquired by Trapping, stunning Rabbits with a Stone, or shooting a Rabbit. Each Rabbit Carcass will have one pelt, along with meat and Fresh Guts.