This is happening to everyone at my organization.
I have the same issue. When in full screen mode, the Pulse Secure Terminal Services Client disappers from the taskbar.
I am on Windows 10 Pro 1903 and have Pulse Secure Terminal Services Client version 8.1.14.59737. The file dsTermServ.exe is served from my User Profile's App Data -> Roaming.
How can I update the Pulse Secure Terminal Services client?