The roller in the machine is steel, so if it is pressed hard against the blade it will dull it.
Since you don't have anything to lose, I would go to Home Hardware and see if they have a knife sharpener with preset stones that would fit in the die. Like this one:
http://www.ebay.com/itm/Accusharp-Kn...oAAOSwpDdVSUo7
You will need to either spread the foam away from the blades or remove it all together (then replace it with a couple layers of craft foam). You could also take it to a place where they sharpen knives & scissors.
Steel rule dies are sharpened all the time for printing shops, but they use the bigger wooden dies like the studio uses. The dies are removed from the wooden block, then sharpened and either replaced in the original wood block, or a new block is made. The GO dies are embedded in the plastic base so this isn't an option for them.
Oh, and I just figured out where the space goes in your name!