Its position is being based on some combination of with width and height. You need to make it fixed, not fluid.
Need some actionscript to provide any help with coding, but it should be something like this
text_mc._x = Stage.width - 200; // puts the clip 200 pixels left of the window edge
text_mc._y = Stage.height - 150; // puts the clip 150 pixels above the bottom
Obviously you need to find the place where the flash video resizes the stage, and apply the correct numbers for your clip based on its height and width.