I don't know if this will work, but it's worth a try.
You can try adding the caching code to the file. You usually do this by adding a random string of characters to the end of the file name, for example. new URLRequest("bigFile.foo?uncache=273095285209750"). For you, instead of using a random string, you can use a date object to generate a string. For instance...
var now:Date = new Date();
var request:URLRequest = new URLRequest("bigFile.foo?uncache=" + new Date(now.year, now.month, now.date));
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