More information for this situation:
The Servers are all 2012.
It makes no difference if the machines that won't connect use remoteapp or remote desktop.
The users have licenses assigned to them.
In looking through the RemoteDesktopServices - RdpCoreTS event log on one server I see a series of event ids at the time that one of the users having the issue created.
The next to last event id was 132 - A channel XPSRD has been connected between the server and the client using transport tunnel: 0. @ 11:00:44 AM
The next entry in this log is event id - 102 - The server has terminated main RDP connection with the client. @ 11:07:01 AM
Looking is the TerminalServices - RemoteConnectionManager event log I see the following:
event id 1149 - Remote Desktop Services: User authentication succeeded: @ 11:06:21 AM
Then there are 3 event id 1152 entries - Failed to create KVP sessions string. Error Code 0x8007007A @ 11:06:23 AM, 11:06:25 AM, 11:07:01 AM
I find these last strange as he has an assigned license and I have followed all instructions about making sure that the licencing server is set up with and in the proper groups.