Why do the screws on my fence snap after install?
Fence boards tend to warp due to extreme sun exposure and changes in moisture levels. This puts a substantial strain on fasteners. If you did not purchase high-quality screws, this would explain the problem. Low-quality fasteners use weak metal alloys and have much less strength than better screws, which would pull through the wood before they'd break.

You can add new screws as needed or pull and replace them with better screws all one at a time (to avoid having to reposition boards).