that happened to me. i use the blue painters tape and it would pull off paint. I found that would happen when the paint didnt dry enough, also if i put on a coating without letting the layer below it fully dry.
I agree that the clean release is the way to go.. I was having problems using the blue stuff when I started painting as well.. I have seen the clean release in both the purple and the off-white colors.. The only problem that I have had with it is sometimes it does not stick well enough.
another trick i learned was to take the tape and dab it on your forehead a bit. the oils will weaken the adhesive enough so that it will mask the area off and not adhere to the paint. you can also use a t-shirt as well to dab on.
I have herd that electrical tape works well. I have used it twice on a round piece I painted and it worked perfectly. No peeling or bleeding. But I have never tried it on a flat piece before. Also You should take the tape off before it dries so it can't peel.