The psalmist is parched and his only hope is moisture if the skin is to survive. How does he cope? What can he do? Notice these words:
He longs for God to deliver (119:81a).
He hopes in God’s Word (119:81b).
He does not abandon God’s precepts (119:87b).
He petitions God to preserve him (119:88a).
The image the psalmist uses, the drying, parching wineskin, impresses me: it is so evocative of sterility and frigidity and apathy and depression and hopelessness.

In spite of his condition, the psalmist has the hope of a wineskin — which (of course) has no real hope, but it can signify (by metaphor) a condition of serious need. He longs for God’s deliverance.
One thing strikes me about the Bible: living by faith occurs when there is a challenge beyond our capacities, living by hope occurs when we are hopeless. It is easy to talk about faith and hope; it is hard to live by faith and to live in hope. The psalmist points the way.