The Docker daemon (on the Docker application Droplet) is run with the default open file descriptor limit `ulimit -n` of 1024. This is inadequate for many services (Redis, in my case.)
Because it cannot be changed within the Docker container, the Docker daemon itself must be run with a higher limit.
Please alter the Upstart Docker script "/etc/init/docker.conf" to set a high er limit. For example:
description "Docker daemon"
start on filesystem
stop on runlevel [!2345]
# set max file descriptors to 65536 (soft/hard)
limit nofile 65536 65536