Thanks for the report. I'm not familiar with how flash handles saving data. Does the URL have to match exactly for it to work? We use ever-changing expiring URLs on flash content to prevent people from hot linking our SWF files, but that might be causing the reloading issue.
Regarding the browser caching issue, the expiring URLs would definitely be the cause of that. I'll have to explore some options to see if there's a better solution.