Las sesiones no se conservan entre servidores. Microsoft menciona de una alternativa para conservar el estado en estos casos:
Cita: Managing Sessions Across Multiple Servers
ASP session information is stored on the Web server. A browser must request pages from the same Web server for scripts to access session information. On cluster of Web servers (where many Web servers share the responsibility for responding to user requests) user requests will not always be routed to the same server. Instead, special software distributes all requests for the site URL to whichever server is free, a process called load balancing. Load balancing makes it difficult to maintain session information on a cluster of Web servers.
To use ASP session management on a load-balanced site, you must ensure that all requests within a user session are directed to the same Web server. One way to do this is to write a Session_OnStart procedure that uses the Response object to redirect the browser to the specific Web server on which the user's session is running. If all links in your application pages are relative, future requests for a page will be routed to the same server.
For example, a user might access an application by requesting the general URL for a site:
http://www.microsoft.com. The load balancer routes the request to a specific server, for example, server3.microsoft.com. ASP creates a new user session on that server. In the Session_OnStart procedure, the browser is redirected to the specified server:
<% Response.Redirect("http://server3.microsoft.com/webapps/firstpage.asp") %>The browser will request the specified page, and all subsequent requests will be routed to the same server as long as specific server names are not referenced in the original URLs.
Yo lo que hago es redireccionar a una página donde por medio de un formulario se envíen los datos de la sesion por POST. Como es un redirect y solo tiene el envío del formulario no me a causado problemas de que en el cliente se queden los datos, aunque sigo haciendo proebas referente a ello.
Saludos