IMHO, the main problem is with old site forms , cookies etc ... although the net browsers are updated. To be honest you don't know what was updated because of the automatic process and the old soft can be still keeping there. And therefore all starts working properly if you re-loaded the site. Just your net browser updates current cookies, site forms etc... in other ways if the server keeps new site forms etc.. and your net browser isn't updated it may display the site incorrectly.
However it might be the problem either with 32/64 bit soft or the net connection speed as you suggested.