When you SSH into a remote host with agent forwarding (ssh -A) and start a tmux session, everything works fine. But when you disconnect and reconnect later, SSH agent forwarding stops working inside your existing tmux session.
Each time you SSH in, a new authentication socket is created at a path like /tmp/ssh-XXXXXX/agent.12345. When you start tmux, it captures this socket path in SSH_AUTH_SOCK.