(both browsers are used on ebay, PayPal, USPS, FedEx and a very few other sites only. I have no problem restarting (or starting days? later) Firefox 52, Firefox 31, or Firefox 3.6.24 and staying logged in, but I have both browsers configured to never automatically delete any cookies. In that situation, idle activity may play a role. I think all the keep me signed in box does is control whether certain cookies are created and/or the expirations on them to not leave open logged in sessions when using public computers like at libraries or other places. (Some sites like PayPal, banks,, etc monitor activity and auto logout on idle, but eBay doesn't do that) Login sessions are mostly based on cookies.
