Believe it or knot (pun intended) wash it with fabric softener you can do it with all your lines and then let them air dry :-), and if they get stiff again do the same thing.
If its a long anchor line too heavy for your washing machine, fill a barrel or cooler or bin with hot water and fabric softener and let it soak for a week.
It will become more pliable--but not "like new" pliable.
O yea, if you use your own that has the beater bar tie the ropes in a large pillow case so as not to get tangles up. If you use the local laundry spot they have large machines without the beater but the tumbling/ turning can cause it too.