Alright to begin with,
If you create an movieclip(mc) specially for the border(and use it as such) you can by double click on the mc make a little movie inside the main movie....just try it you will see what I mean than!
this is axectly what pgsmedia said, only I thought I would give you a bit of a step by step thingy.
Then if the border isn't inside an mc on its own....well it's getting kinda complicated then...and I can't help you without seeing the .fla file or the actionscript you are using, or an explanation of the structure....
anyway, if this doesn't solve the problem...post the structure