We see similar issues with Smart Cards using the ActivClient software and this is starting to look like an ActivClient software problem.
We notice issues where in View sessions if you try to use a smart card separate from the one you used to log into a session it can cause AC to deadlock and never read any future smart cards forcing a reboot of the VM to reload the software + driver.
What seems to help us is when you are switching cards, allow the card to be read fully by the system before trying to use it. It seems to cause the least amount of issues.
We encountered the same issue in our vSphere 6.7 Update 3 environment. Our team was able to find a workaround that allowed us to use our Administrator card through the VMRC console and will post below in case others encounter this issue.
If you click on the double chevrons in the upper right hand corner of the VMRC console window, you will see all the devices that are currently connected or are available to pass-through to the VM. You should see two separate Smart Card icons (one that looks like an ID card and the other that looks like a door), one will be labeled as the builtin Smart Card reader and the other will have the word "Shared" in front of the Smart Card name. You need to use the one that DOES NOT say "Shared" in front of it. In our case we selected 'Broadcom 5880' versus selecting the 'Shared Broadcom Corp Contacted SmartCard 0' and it allowed us to pass-through the Administrator card and recognize the certificates.
I'm still trying to wrap my head around why this occurs. Maybe it's the type of smartcard or possibly a compatibility issue. It's an easy enough work around but If anyone has any explanations I would very much like to hear why!
We currently have vSphere 6.7 update 3 installed, VMRC version 10.0.6 and current version of VMware Tools installed.
we noticed the same fix. you need to use dedicated (disconnect from host) not shared