A well-cared-for sling lasts five to fifteen years. Here's how to get the upper end of that range.

A quick hose-down once a week keeps salt, pollen, and pool chemistry from settling into the weave. Thirty seconds per chair.
Once a season, take the cushions off and give the slings a full wash. A soft scrub brush, mild soap, garden hose. For stubborn mildew on Sunbrella® fabrics, a dilute oxygen bleach solution (never chlorine bleach) is safe.
Never do this
A breathable furniture cover extends sling life by three to five years. Fully wrapped plastic tarps trap moisture and grow mildew - choose a cover that wicks and breathes. If you live where winters are harsh, store chairs in a garage or shed; if you can, remove the slings and store them flat in a dry place.
Mildew doesn't grow on sling fabric itself - it grows on dirt, pollen, and organic matter that settles on the surface. Keep the surface clean and mildew stays away. For existing mildew, a soft brush and a 1:10 solution of oxygen bleach and warm water removes it. Rinse thoroughly.
Signs a sling is ready for replacement: