It depends. You can apply for most Special Permits year after year. However, you cannot apply for the Any Moose, Any Ram (bighorn sheep), or Mountain Goat Special Permits year after year if you harvested or failed to provide a hunter report under one of these permits. For mountain goats, you can apply again if you harvested your goat prior to 1999.
These three categories have the once-in-a-lifetime restriction. However, you can apply for other categories for these species year after year such as the Antlerless Only Moose or Adult Ewe Bighorn Sheep.
3rd of January, 2014