This is only really necessary if your brick line is made from cotton string. Cotton string is susceptible to damp, rot, and mildew so keeping it dry will prolong its working life. Brick lines made from nylon or other synthetic plastics are waterproof and will not rot.
Don’t over-strain your brick line
You will need to pull your brick line taut to get an accurate line when laying bricks, but over-straining the line may stretch it or even snap it. So be careful.
Storage
Wrapping your brick line around your line pins between uses keeps the string and pins together and at hand for ease of use. Storing your pins and line in a tool box will protect them from the elements.