Indoor moisture created by humidity from the dryer can soak through wood in the walls and cause exterior paint to peel. Exterior moisture released by a dryer vent can get underneath the paint and cause it to peel. Heat from a dryer vent also can cause bubbling in new paint, which can lead to peeling later on. Sometimes, a new coat of paint also starts to peel off the surface of an older coat of paint if the area was not cleaned before the new paint was applied.
Check, or hire an expert to check, that the dryer vent is well-sealed and not leaking moist air inside of the wall. Look for swollen and warped drywall or wood around the dryer vent as a sign of a broken seal. Make sure the caulking around the vent is intact. Waterproof caulking around the dryer vent opening in the wall can help prevent moisture from getting into the opening and soaking into the wood, causing peeling.
Proper painting technique prevents peeling, although the area around the dryer vent might need occasional touch ups. Paint the wood with a water repellent, then paint the wood with an oil-based primer, allowing the primer to dry thoroughly. Do not wait longer than two weeks to apply the paint top coat. Paint the top coat with a latex-based paint. Latex paints are more flexible and less prone to cracking and peeling than oil-based ones. Choose a high-quality paint. Apply two layers of paint, allowing the first coat to dry thoroughly before the second application. After painting, do not use the dryer for a couple days to prevent bubbling from the temperature change near the dryer vent.
Fix peeled areas by removing loose paint, preparing the wall for new paint, then repainting the area. Scrape off peeling paint. If the paint left depressions where it peeled, use a putty knife to fill in these with spackling. Sand the area with 150-grit sandpaper. Treat the area with a water-repellent preservative, and prime unpainted spots. Paint with a top coat that matches the rest of the paint.