The best way to maintain your synthetic winch rope is to protect it from environmental damage. UV rays from the sun and long-term exposure to moisture are both things to be avoided if you want a nice long lifespan for your rope.
As far as UV damage is concerned, try to keep your rope out of direct sunlight where possible. If you don’t use it very often, you could consider removing the rope and storing it in the garage until you do need it again.
Avoid moisture damage by never storing the rope wet. If it gets wet during use or when driving, remove the rope and lay it out to dry properly before storing it off the vehicle or rewinding it onto the drum.