Tricks to getting the striping tape to stay secure:
The first trick is to place the tape onto slightly damp nail polish (ie: NP is still tacky). Make sure you position it correctly first go, because if you move it about it will smudge and drag your NP.
Cut the tape longer than you need it to be...about 1cm excess overhang is fine.
Get some nail glue and a toothpick and add a tiny bit of glue on the side edge of your nail where the tape will go. After you've done that, you need to grab the excess tape ends and "wrap it" around and under your nail. If the tape is near the cuticle, get some nail nippers/clippers (or very fine pointed manicure scissors may work) and cut the tape to length immediately after pressing it into the glue. Keep the end pressed down with a toothpick and count to 10.
For the tape hanging over the end of the nail, you'll need to get a buffer (I always use a sausage buffer) or a soft/medium grit nail file, and file the excess tape off the edge of the nail. File in one direction in a downward motion (if you file at an angled/curved downward motion, that will remove any minuscule bits of tape sticking out which will catching and cause lifting).
Add topcoat, and be sure to go around the edge/rim of the nail with it. That will "seal" it. You can do two coats of topcoat if you wish, but I tend to put a coat of topcoat on every day to keep it in place and the design looking shiny and new. If you do that, the striping should easily last a few days without problems. If you start to get lifting, glue the edges down and seal with topcoat. I've had striping nail art last a week.
Do not add more than a little amount of glue. If there's a noticeable amount of glue piling up around the tape leaving bumps, you'll need to wipe it off with a cotton bud/q-tip. Do this quickly and carefully. You'll eventually get to know exactly how little glue to add after you've done this a few times.
Another trick to keeping striping tape secure is to add a rhinestone (or several) on top of it. This is especially good to do in the cuticle area because you won't have the problem of the stones falling off as easily as if they were on the end of your nail. Secure stone(s) on top of your tape with a tiny drop of clear topcoat, put stone(s) in place, and go over the nail with topcoat. (for example, see the pic below - the tuxedo on the left, I added three stones to secure the tape in place.)
If it's all too hard to understand, please let me know. If I get time today, I'll take some pics of what I mean.