Some pages (eg. all that use the consent.truste.com script) use localStorage to store the decision.
That way the decision remains client-side and can still be persistent by hiding the question via javascript.
This law applies to any kind of "data" stored on the client, so using localStorage to store the user's answer would be breaking the law.
http://www.cookiepedia.co.uk/eu-cookie-law
I don't remember the specifics.
They could add a checkbox "store this decision locally", which would allow storing this single information - and localStorage is the best place to put it (unlike cookies).