As we all know, stickers are the most disliked feature of Lego sets. But they are also a necessary evil so, in case I might be able to help, I'd like to offer some thoughts.
First, all stickers are not created equal. If your sticker sheet is the type that uses a clear film you are doing well. These sheets, as are found in the older train sets, seem to be wonderful. These stickers STICK, and do not ever seem to lift. However, if the sticker sheet is printed on a white film, you may or may not have good luck. Some work fine, while others are a nightmare. I had to rebuild my Tiny Turbos "Tuner Garage" twice because the stickers lifted and cracked. But the most recent application is doing well, some three years after the stickers were applied. Why?
At any rate, I have found this application technique quite useful. I first cut a small strip of the sticker backing paper, from an unprinted section of the sheet, to use as an application tool. Remove any sticker film from the strip. Next, gently bend the sticker that you want to apply at one end. This will cause the sticker to pop up from the sheet at that one point. Now slide your application strip under the edge of the sticker with its glossy side up. Your sticker should now be resting on a part of the original backing sheet, just as it was printed. Now grab the sticker/strip sandwich and lift the sticker from the sheet. Now you have a sticker with a "handle" so you can avoid touching any of the glue with your fingers. Also, the "handle" greatly aids in positioning the sticker which, in turn, helps to eliminate the dreaded air bubbles that can ruin the entire operation. I use a magnifying lens with a built in light to help in positioning and centering. Once you are satisfied with the placement, slowly press the sticker to the surface working towards your handle. The gently roll the handle from under the sticker and continue to press the sticker in place. DO NOT PULL the handle from the sticker or you will pull some of the glue from the sticker. Not good.
Presto. Sticker perfection.
Also, though I use cotton gloves to assemble my sets ( my fingers are too oily ) I NEVER use them while applying stickers. You would be surprised how easily the sticker glue attracts fibers from the gloves.
Now then, if anybody out there knows how to prevent the "white background" stickers from lifting, please let me know. I have read about the lifting/cracking phenomenon in the 7163 Star Wars set. I don't have that set yet, but I don't want to buy it if I can't apply the stickers without worry.
Could the problem be low humidity? And "Thank you"!