This has always been a problem with the small center edge pieces on my gigaminx. I keep it in my backpack and they tend to fall off just a few weeks after I apply them. Is there any way to prevent this other than keeping it on a desk?

To restick a troublesome sticker, I remove the sticker, clean the surface carefully and apply a few very tiny drops of superglue to the outer edges of the sticker area. I use a superglue that is purple when it is wet, so I can see where it goes. Please note that if you ever scrape off the sticker, you will find some minor cosmetic damage to the surface of the piece.

A more permanent solution is to get a good quality replacement sticker set. I'm very happy with the Cubesmith stickers on my Gigaminx.

Finally, I carry puzzles around in a soft pouch or bubble wrap.

I always get cubesmith stickers and it still happens, and it would still happen when I kept it in a little silk pouch you get for free with skull candy headphones. I guess superglue would work but I'd really rather avoid something THAT permanent in case I want to change sticker colors. To be realistic I'll probably end up doing that eventually

With small dots of superglue the sticker can still be scraped off very easily. It sounds like you need an inner box to carry your puzzles in your backpack .

I could suggest to buy stickers from me, but unfortunately it won't solve this problem.
Even with the best quality stickers the really small ones will easily fall down.

With Shapeways WSF, I know the ironing (or heating with a hair dryer) is a good solution.
But with a Gigaminx I don't know will it work or not.

The only solution I know was already mentioned by Pete. Use superglue! If you use it carefully, there will be no mark of it, and the small stickers will hold.