Some more information: the issue has just occurred, again on an instance without the "service_count = 0" configuration directive on pop3-login.
I've observed that while the issue is occurring, the director process goes 100% CPU. I've straced the process. It is seemingly looping:
......epoll_ctl(13, EPOLL_CTL_ADD, 78, {EPOLLIN|EPOLLPRI|EPOLLERR|EPOLLHUP, {u32=149035320, u64=149035320}}) = 0epoll_ctl(13, EPOLL_CTL_DEL, 78, {0, {u32=149035320, u64=149035320}}) = 0epoll_ctl(13, EPOLL_CTL_ADD, 78, {EPOLLIN|EPOLLPRI|EPOLLERR|EPOLLHUP, {u32=149035320, u64=149035320}}) = 0epoll_ctl(13, EPOLL_CTL_DEL, 78, {0, {u32=149035320, u64=149035320}}) = 0epoll_ctl(13, EPOLL_CTL_ADD, 78, {EPOLLIN|EPOLLPRI|EPOLLERR|EPOLLHUP, {u32=149035320, u64=149035320}}) = 0epoll_ctl(13, EPOLL_CTL_DEL, 78, {0, {u32=149035320, u64=149035320}}) = 0
FD 13 is "anon_inode:[eventpoll]"