The Floral Shirt spoils after 15 days similarly to the Fashion Melon and the Garland instead of losing durability as it's worn, thus it cannot be repaired with a Sewing Kit. Storing it inside an Insulated Pack or Snow Chester will slow its spoilage rate.
Since the item requires Cactus Flowers to be crafted, it cannot be crafted until the first Summer. Unfortunately, it only lasts for 12 days after that, due to the 25% faster spoilage during Summer.
Trivia
The Floral Shirt used to be crafted using Petals, Silk, and Butterfly Wings, and it wasn't as effective against heat.
Even though it requires a Cactus Flower to craft (suggesting that is the flower on the shirt), typical "Hawaiian" shirts depict the Hibiscus, the Hawaiian state flower.