The issue of the white latex paint on the outside wood rail cracking and blistering when exposed to rain, then softening and blistering further with subsequent rainfall can be attributed to poor adhesion and moisture penetration. To resolve this issue, it is crucial to address the root cause and implement appropriate corrective measures.

1. **Surface Preparation:** Properly prepare the wood surface by ensuring it is clean, dry, and free from any contaminants such as dirt, grease, or old paint residues. Sanding the surface to create a rough texture can also promote better paint adhesion.

2. **Primer Application:** Apply a high-quality bonding primer designed for exterior wood surfaces. The primer will help create a strong bond between the wood and the paint, improving adhesion and durability.

3. **Quality Paint Selection:** Choose a high-quality exterior latex paint suitable for outdoor use. Look for paints that offer good adhesion, flexibility, and moisture resistance to prevent cracking and blistering when exposed to rain.

4. **Proper Application Technique:** Follow the manufacturer’s instructions for proper paint application, including the recommended number of coats and drying times. Ensure the paint is applied evenly and in optimal weather conditions to facilitate proper curing.

5. **Protective Coating:** Consider applying a clear protective topcoat over the painted surface to enhance durability and water resistance. This additional layer can help shield the paint from moisture and prevent blistering and cracking.

6. **Maintenance:** Regularly inspect the painted wood rail for any signs of damage or wear. Promptly address any issues by performing spot repairs or repainting as needed to maintain the integrity of the finish.