This may sound crazy, but I had the same exact problem and this is what worked for me.
I have security suite software installed on my computer, as most of us do, and well, although it is NOT recommended, I temporarily disable the firewall. Wait for the little icon to appear in my taskbar telling me my firewall was disabled, then I opened my browser to ECF. I typed in my username and password and checked the little box that say "remember me" or whatever and of course, I was logged in.
I then went and turned my firewall back on, and Voila! No issues what so ever.
I have to repeat this every time I delete my browsing history and cookies, which is only about once a month. But I will take that any day over having to log in every 3 minutes like I was.
HTH...........................
