You'll probably get better with some practice so that it doesn't happen as often.
Always pay attention to the "direction" the design is facing. Try to avoid peeling directly perpendicular toward the long part of a letter, for example a capital "L." Peeling left to right puts a lot of pressure all along the long part of the L and may be enough to lift it up. I'd prefer to peel from lower left so that I hit the L at the pointy part. You want to peel an "e" right to left so you peel away that little bit of vinyl inside the lower part of the e with the rest of the vinyl. Going left to right, it will leave that bit of vinyl, but as you pass the e, that bit may lift up and take the rest of the letter with it. On the other hand, other letters like a "g" need to be pulled the other direction.
None of this is set in stone. Using my examples, peeling the word "Leg" would be virtually impossible. In reality, I usually start in a corner and peel at an angle. From there I can adjust the direction I'm peeling if I need to. If I get to a certain shape and want to pull right to left, I start doing that. Then if I get to another that will peel better from bottom to top, I do that. And if I get to one that I'm pulling from completely the wrong direction, I just hold it down with my finger and peel away.
It sounds harder and more involved than it is. With practice, you'll just look at a design and start peeling from the best direction without even thinking about it.