Hi, I've looked at the sites. I manage to repoduce the error if I entered the "/edit" area with an url not starting with "www". Doing this can cause the preview to not function properly.
What happens is that there is set up a primary domain in the site module that redirects all visit requests to the primary domain. This redirect does not happen for the "/edit" area. What we end up with is a preview frame where the domain differs from the surrounding frame, and sometimes this cause javascripts that refreshes the frame to fail, due to cross domain security mechanisms built into the browser.
The quick workaround is to make sure you enter the "edit" mode with a url that matches one of the primary domains of the site. In the "styreinstitutt"example, use: http://www.styreinstitutt.no/edit not http://styreinstitutt.no/edit
In a furtue update, we'll change the preview so it work as expected regardless of the URL you use. It's high up on the list, so expect a fix for this before 01.10.2011