Not trying to bring this post back from the dead, but while working with ESRI support on this issue with a Citrix server (users crash or log out, arcgiscachemanager.exe doesn't close out 20-30 minutes later or more if at all, users cannot get back in to ArcMap and then they have to rely on on of 2 server administrators to be available to log into the server and manually release them), ESRI is copying and pasting a solution from this page and it doesn't work. At least not when working in a Citrix environment.
For Citrix, we found that creating two registry keys (one for killing the hung process, one for pushing settings back to their original state) "fixed" the issue.
For non-Citrix, we've toyed with the idea of just creating a script to kill the process, but since when we are not in Citrix, we are already on the server, we decided it wasn't necessary.
Hope this helps.
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Citrix has registry key settings that will help manage applications that spawn secondary processes in the background. You have a lot of the symptoms that should make this solution a plausible setup. Have a look through the following Citrix Knowledge Articles:
Graceful Logoff from a Published Application Renders the Session in Active State: http://support.citrix.com/article/CTX891671
Active Sessions after User Logs Off in a XenApp Environment when Upgraded from Windows Server 2003 to Windows Server 2008: http://support.citrix.com/article/CTX134956
XenApp 6.5 AppCenter Console Displays Application Status Application Not Running: http://support.citrix.com/article/CTX133328
In these articles, it discusses how published applications can cause a session not to close or a user not being properly logged off. In those cases, sessions had to be reset/exited by an admin or by terminating the process from the server that was still running. What happens in Citrix is that you publish the main application, in your case ArcMap. Only that exe is closed when exiting an application (or if it crashes). As a result, any exe's associated with the application that were spawned when the application was opened are not be fully closed out in Citrix resulting in this state. So when the ArcGISCacheMgr.exe takes a long time to execute or the application crashes your end users are left unable to start a new session.
The articles discuss how you can add these secondary processes to a registry key to close them automatically on close of the main application. Another option you can explore is a logoff script to check for the processes and terminate them if they exist.