I keep breaking my jump rope

I have a weighted jump rope that I like, but it came from Wal-Mart, which is probably the problem. It keeps snapping in half right in the middle on really cold days. I work out in a storage building with a concrete floor that has epoxy on top, and this epoxy has paint chips sprinkled in. I have wondered if the cold (sub-30 degrees) combined with the abrasiveness of the paint chips and the impact of it on the concrete is making it snap. Should I get a different rope? Should I put a piece of carpet or rubber down on the concrete? I love using it, but this is the second one I've snapped.
 
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