Turns out docker only restarts unhealthy containers when running in a Docker Swarm setup.

For other setups, the following crontab entry provides a quick and dirty alternative that checks for unhealthy containers and restarts them.

*/15 * * * * /usr/bin/docker ps -q -f health=unhealthy | /usr/bin/xargs --no-run-if-empty -L 1 /usr/bin/docker restart