Has this always been a problem?
Did you replace the VC ssl certificates with new ones?
Is the ESX server swapping heavily or low on disk space?
run a "free -m"
run a "df -h"
Have a look at the vpxa and hostd logs on the ESX server at the time of the disconnects for any errors/warnings:
/var/log/vmware/vpx/vpxa.log
/var/log/vmware/hostd.log
Try to re-create the ESX/i SSL certs:
1. If enabled, disable Virtual Machine Auto-start through the VI Client by clicking the host --> Configuration --> Virtual Machine Startup/Shutdown --> Properties
2. Disconnect and remove the host from VC by right-clicking it in the VI Client and choosing Disconnect then Remove
3. Login to the ESX server and stop hostd: service mgmt-vmware stop
4. Backup the old certs:
mkdir /root/ssl-old
cp /etc/vmware/ssl/* /root/ssl-old
5. Delete the certs: rm -rf /etc/vmware/ssl/*
6. Start hostd: service mgmt-vmware start
7. Reconnect the host to VC through the VI Client
8. Re-enable Virtual Machine auto-start if it was enabled.
