Norton shouldn't have any effect on your browser cookies I would think. Check to see if FF is set to automatically delete cookies upon closing.
FF>Tools>options>privacy
If that isn't the problem, check within Norton's options to see if there's a privacy setting which deletes cookies.
That said, there are better free Anti virus options than McAfee and Norton. I highly recommend Avira personal.
www.free-av.com
You can visit
www.av-comparatives.org for AV testing results.