I was running into this problem this weekend, and found if I starched the fabric, the freezer paper didn't like it. Normally it sticks pretty well - you don't want to "under" or "over" heat it though. You might want to get a new roll, or try the roll you have on a different fabric. Perhaps it's the line you are working with??
Good luck. I'm starting my Dear Jane early next year. I'm debating about fabrics and want to make sure they are perfect - this is going to be a long process and don't want to hate the fabric half-way through!