I found something that is working for me. I have two computers in two different locations, both Win7 and the latest version of FF. Today, on computer A, I refreshed FF and installed LP from the LP website for the FF plugin version,( I DIDN'T update LP from the FF addons) It installed 22.214.171.124. I frequently open and closed the browser on that computer throughout the day and it stayed logged in every time! I later went to computer B and just updated the plugin from 4.7.1 to 126.96.36.199 without refreshing FF and I had he same problems as before when LP would log me out almost every time I closed FF, then reopened the browser. I then refreshed FF on computer B, installed LP from the LP website and so far, no issue with logging me out! Maybe refreshing FF is the key? Hope that works for you.