Modern dacron sails have two enemies: direct sunlight and abrasion: direct sunlight will degrade and weaken the cloth given the chance. Abrasion will make the threads part and cause tearing in the long run.
Make sure sails are absolutely dry before storing them!
Never leave a sail flapping in the wind for any length of time. This, like abrasion, weakens the fibers.
Use only clean water to wash your sails. Hosing them off is the most effective way. Never put them in a washing machine, or use harsh chemicals.
If you discover any small holes or rips, fix them immediately by applying sail tape to both sides. Bigger damage should be repaired as soon as possible.
Avoid stuffing wet coloured sails into a sailbag. The colour could transfer.