Symptoms:

• A proxy server is being used to provide internet connectivity for the vCenter Server.
• The proxy server is configured with the same TCP port for both HTTP and HTTPS traffic.
• Skyline Health in vCenter shows a warning "Online health connectivity" similar to the screenshot below:

VMware vCenter Server 7.0.x
VMware vCenter Server 6.0.x

If the proxy is configured to use the same TCP port for both HTTP and HTTPS traffic, 

• open an SSH connection to the vCenter Server Appliance
• create a backup of the proxy configuration:

  # cp /etc/sysconfig/proxy /storage/core/proxy.bak

• edit the file:

  # vi /etc/sysconfig/proxy

• find the line starting with HTTPS_PROXY="https://..." and change this to HTTPS_PROXY="http://..."
• find the line starting with NO_PROXY
• edit this line and add both the fully-qualified domain name and the IP address of the vCenter Server to this line

NOTE: Please be aware that the entries in NO_PROXY need to be separated by a comma followed by a single space. Only using a comma as separator is not enough. Also, should when considering to exclude a whole domain from the proxy settings, be aware that NO_PROXY requires a specific syntax, meaning instead of using "*.domain.tld" or just "domain.tld", ".*.domain.tld" needs to be used.

Example: given the vCenter is vc.domain.tld, has the IP address 192.168.1.55, the proxy is proxy is called "proxy.domain.tld" and the port it's using is TCP 8080 for both HTTP and HTTPS traffic, this is how the /etc/sysconfig/proxy should be looking:

# Enable a generation of the proxy settings to the profile.
# This setting allows to turn the proxy on and off while
# preserving the particular proxy setup.
#
PROXY_ENABLED="no"

# Some programs (e.g. wget) support proxies, if set in
# the environment.
# Example: HTTP_PROXY="http://proxy.provider.de:3128/"
HTTP_PROXY="http:/proxy.domain.tld:8080"

# Example: HTTPS_PROXY="https://proxy.provider.de:3128/"
HTTPS_PROXY="http://proxy.domain.tld:8080"

# Example: FTP_PROXY="http://proxy.provider.de:3128/"
FTP_PROXY=""

# Example: GOPHER_PROXY="http://proxy.provider.de:3128/"
GOPHER_PROXY=""

# Example: SOCKS_PROXY="socks://proxy.example.com:8080"
SOCKS_PROXY=""

# Example: SOCKS5_SERVER="office-proxy.example.com:8881"
SOCKS5_SERVER=""

# Example: NO_PROXY="www.me.de, do.main, localhost"
NO_PROXY="localhost, 127.0.0.1, vc.domain.tld, 192.168.1.55"

Or, if you want to exclude the traffic to the complete domain from being routed through the proxy:

...
# Example: NO_PROXY="www.me.de, do.main, localhost"
NO_PROXY="localhost, 127.0.0.1, .*.domain.tld, 192.168.1.55"

Please see https://kb.vmware.com/s/article/1020302 for how to edit files on ESXi using the VI editor.
The problem described in this article can also lead to other issues, such as the one described in https://kb.vmware.com/s/article/2149196 .