Modern hubs and skewers are designed around vertical dropouts, and lack enough holding power for horizontal dropouts.
You need to improve the bite enough to keep the chain from pulling the axle forward.
Better skewers are a step in the right direction and will help, but if you ride steep hills it might not be enough. I prefer to get bite from the axle faces, using hardened serrated lock nuts where possible. Otherwise, I "glue" coarse grit to the face with a nylon based nail polish or similar.
There's more than one way to solve this, but they all involve improving the grip of hub and/or QR into the dropout.
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