Each of the services in Nutanix Cluster has a definitive purpose. Nutanix ClusterHealth service, for example, is practically an in-build monitoring system of the cluster. Nutanix Cluster Checks (NCC) and pre-upgrade checks rely on ClusterHealth.
As with troubleshooting of any service status, the first thing to do is to attempt to start the service manually from the CMV.
If that does not help and you are not running Hyper-V on the host check the logs located at /home/nutanix/data/logs/ for any FATAL files and inspect records in there.
Note: Foundation process does not run when the Node is a part of a Nutanix cluster.
For logs location, handy commands and more tips be sure to check KB-1518 NCC Health Check: cluster_services_down_check. While the article is on an NCC check the troubleshooting steps and commands apply to the ClusterHealth service as much as to other services.