All other requests to the server include the cookie, which has the sessionid and lets the load balancer know which server to stay on, except for the post to the AjaxFileUploadHandler.axd. I have put two screenshots from fiddler so that you can better understand what I mean.
POST /AjaxFileUploadHandler.axd?contextKey={DA8BEDC8-B952-4d5d-8CC2-59FE922E2923}&fileId=3AE2923C-8010-0953-2918-628F9725CD0F&fileName=Chrysanthemum.jpg&usePoll=true&storeToAzure=false&acn= HTTP/1.1
POST /AjaxFileUploadHandler.axd?contextKey={DA8BEDC8-B952-4d5d-8CC2-59FE922E2923}&fileId=3AE2923C-8010-0953-2918-628F9725CD0F&fileName=Chrysanthemum.jpg&usePoll=true&storeToAzure=false&acn= HTTP/1.1