This has happened to me, only when using BB. I tried FrogTape since i had it on hand from a painting job, and it seemed to work better (especially the delicate one). Those aren't cheaper though, about the same if not a tiny bit more.
Honestly I've stopped taping over everything, and then attaching the pattern on tape. Yeah it's a little bit easier to pull off in the end, but it takes extra time and money to put it all on in the beginning. Now I just give the pattern a good spray of adhesive and slap it right on the wood. Maybe roll over it with or dowel or your hand to make sure it's really on there and you're good! It doesn't peel, even on delicate areas.
Take a towel, rag, or whatever you want with some mineral spirits when you're all done cutting and the pattern peels right off. You do have to let the mineral spirits dry, but it's not that big of a deal. Maybe like 30 minutes.
Maybe give it a try, at least when you cut BB.