My first bet would be that you are not watching for EINTR as a result of $sock->accept. The first time through the loop, the connection is accepted and a new process is spawned to handle the connection. Once this process dies, the caller receives SIGCHLD, which causes accept() to be interrupted, which should result in $! == POSIX::EINTR(). If this is the case, the accept() should be restarted within your code.
On an unrelated note, there are a few error cases that you don't check, such as the initial fork() in start_daemon() returning undef, etc.