Hi,
But sorry for a moment, if no one else has answered you maybe it's because no one has encountered a problem as particular as yours or they solved it by involving the technical support services of VEEAM & VMware. The only thing you say is that the vCenter object is "unreachable", but you don't say once you "reboot" if the logs show some indication of error or you checked the status of the services through the console of the vCenter object (call it DCUI or whatever you prefer).
You say that to regain control of your vCenter object you have to reboot the host system which means, HA (just to say) move it to another host or you have to reboot it brutally.
If you have reinstalled the VEEAM and VCSA objects and in any case the problem has remained exactly the same, perhaps there are other ulrelated causes.
The point of my speech is that a forum does not replace the technical support of the software manufacturer because the similarity of a very specific / particular problem does not imply at all that the causes are the same.
Regards,
Ferdinando