When I launch Internet Explorer as a Terminal Server published app, sometimes it thinks that it has closed down and logs me off automatically.

The wnssoclient can take care of this. 
Set your start program for iexplore.exe 
Pass in the URL you want to launch as a parameter 
Then for the SSO script use : 
{alsowaiton:iexplore}|{logoffonexit}|{notimeout} 

This will wait for iexplore to finish before issuing a logoff. 

The reason for this is that based on some settings for IE, it launches itself and then launches another sub process for the site you want to browse to. This double launch causes wnssoclient to think you finished with iexplore.exe and logs you off. 

The alsowaiton:iexplore tells it to wait for another iexplore to finish before shutting down. 

To pass in a URL to have open when IE launches, put http://www.google.com as the parameter to send to iexplore.exe in the webapp.