Once your browser has cached the ban, it'll remember it. That's why you have to clear the cache.
So say you login to forums via banned mobile IP. You now have a cookie stored that says "you're banned."
You now need to clear the browser cache and connect with a non-banned IP, whether that's your home WiFi, your cell carrier assigning a new IP to your phone (as they regularly do), your work or Starbucks WiFi, or whatever.
But connecting on your home network your desktop works on with a device that has a banned cookie, without clearing the cache, results in that.
Make sense? :)