I don't know anything at all about Safari, but here are a few basic suggestions:
Make sure that all your browser-based stuff has the latest versions, so your flash player and java. Usually these update automatically, but you might have that function turned off.
I would also try going into your privacy or history settings and clearing all the data. Also, turn off the option to save history for x number of days. It will be like loading the game for the first time every time, but at least they'll load.
It sounds like a coding issue on our end, though. That perhaps the cookies that store the loading information aren't communicating with Safari very well. Anyway, check your updates and try to browser history thing. If that doesn't work, we'll need to do some more investigating.