Acrobat DC Sign in for all users on Terminal Server

A few quick observations on the information provided:

• Terminal Server is Windows Server 2008 R2 Standard

Support ended for both Windows Server 2008 and Server 2008 R2 since January 2020. Unless I am missing anything regarding extended support , this is what Micrososft announced. There is no more updates or security fixes. but they do have a migration guidance acessible here:  Support for Windows Server 2008 has ended 

• Adobe Product is Acrobat Pro DC (Version 20.9.20074.389258)

Your Client is missing the  last update pushed this month.  I don't think this may be the reason of the issue though.

What I did find for you is explained here: 

Known issues common to virtual installs

• Push notifications to specific users are unsupported.

• If users sign in on both a virtual environment and a physical machine, then they may be randomly signed out from a physical machine. This is because users can activate Acrobat on multiple virtual machines while only two activations are allowed per user. The current implementation provides an over activation workflow for these environments which does not force users to see or interact with any dialogs.

• Volume licenses are deleted when multiple users launch the product simultaneously before it is activated.

• In the Help menu, signed-in users are not shown as signed-in on subsequent sessions.

• Users may appear as signed-in on the Help menu even if they are signed out from the Creative Cloud Desktop application or signed out of the current session.

• Signing in with IDs having no subscriptions may result in random failures.

The information above is taken from : Acrobat Virtualization Guide 

You may also need to use this other reference:  Acrobat DC Deployment Planning and Configuration 

Confirm with  your Client if bullet #2 and #3 of the  Known Issues above is what the problem is.