USNA does not publish the number of LOAs it puts out, even to BGOs, and the number can vary by year. Traditionally, they have gone out throughout the year -- I've seen them as late as early January, although most go out by the end of a calendar year.
However, please remember that LOAs are a very small percentage of appointments. And, you still need a nomination.
Your efforts are best focused on getting an appointment -- if you get an LOA, great, but it shouldn't be your goal.