Ayaapia Kiilhswa (Buck Moon) is one of two lunar months named for the White-tailed Deer. To the best of our knowledge, this month is associated with the end of the rut (breeding cycle) and the older male deer losing their antlers.
Today, there is a lot of variation within White-tailed Deer populations regarding when bucks drop their antlers. It appears that historically, the older White-tailed Deer bucks dropped their antlers after younger males. The loss of antlers marks the end of the rut (the breeding cycle) for these more mature male deer.