It appears to be the lack of shortcuts. After installation all I do is delete or rename the "Symantec Encryption" folder at C:\ProgramData\Microsoft\Windows\StartMenu\Programs and if its missing upon reboot it will try to install or I guess repair like you said.. I put it back with its shortcuts and reboot and all is fine, it does not try to reinstall.
This is pretty extreme considering its merely some shortcuts I'm moving. The shortcuts are forced to be there then? There has to be a way to stop this behaviour?
I can remove the PGPTray.exe shortcut in Startup without it trying trying to reinstall. I installed it for all users, from and to the local disk.
I made a video of the problem if you want to see it in action.