From what I know, permit waits for that trail are often long. The office gets swamped with requests every year. A month is actually on the shorter side compared to some stories I've heard. They have a small team sorting through a huge pile of applications. It's a drag, but it shows how many people want to experience that place. Your permit will likely show up, just later than you'd like.
Is the permit office still using smoke signals to communicate? I mean, a month wait is just the start since I heard some folks wait half a year. They must be sorting apps with a magic eight ball or something. It's good that so many want to see the trail, but the process is a total joke. You'd think with all the fees they collect, they could hire more than two people. But no, we get to stare at the mailbox until further notice.