I'm not aware of an option to do this with HA. What I could think of is to configure the database server service for a manual startup!?
Simply put, this is not a use case for VMware HA, this might be a use case for Fault Tolerance, if the VM specs allow it. VMware HA is a restart, plain and simply, what you are looking for is some kind of replication, as you will lose access to VMs on a failed host.
Your best bet is to create an alarm in vCenter for that VM and check for HA restart event, make it run a PowerCLI script that just turns this VM off.
Also you can create alarms that are not available in vCenter by using the event codes, see my blog: Custom alarms for events in vCenter 5.x | Virtual-Ice
Hope this helps,
I have a scenario where I want HA enabled, but on certain VMs, I don't want HA to restart the VMs on another host if there is a failure, but I want the VMs accessible. The closest option that I saw was setting the VM Restart Priority to disabled, but then if the host fails, there is not way to access the VMs since they will stay inaccessible with the host. We have some databases that management does not want to automatically come back online, so I've been tasked with finding a solution.
I've looked online, but I can't seem to find anything, I also looked at the advanced options, but nothing seems to be an exact match for want I'm looking for.
There is nothing for this within vSphere today, I did file a feature request for this a while back and it is on our "to do list" but not sure when it will make it in the product.