robzilla - 4:35 pm on May 23, 2011 (gmt 0)
According to its response headers, ga.js is cached for a mere 24 hours, so it depends on the other sites your users have visited in the last 24 hours. If you have a lot of return visitors, you can speed up their visits by hosting ga.js locally and having it expire in, say, a year's time. This would be something you could test with the Site Speed feature in GA.
As a result, your users will still have to redownload ga.js once a day when they visit other sites using GA, but on your site they'll only redownload it whenever you've updated it (assuming you've set it up as I described in my previous post).