I believe deck screws are quite brittle, so they snap easily.
Also, you need to consider shear stress (sideways stress). If the panels expand due to moisture at a different rate than the runners, then the screws would be under significant stress due to differential expansion.
Have you built your fence according to a recommended design pattern? For example, when I think of "fence panel", then I think of a complete, self supporting panel that goes between the posts. Typically, panels are fixed directly to the posts, and do not have separate runners.
An alternative design is without panels, where you install the runners, and then fix vertical boards to the runners.