Unlike hybrid tomatoes, heirloom tomatoes have not been tested and bred for disease resistance. For this reason, they may or may not have some natural resistance to various diseases. However, it is beneficial to remember that these unique varieties would not have been saved if they were not both productive and tasty. You can give your heirloom tomato plants the greatest odds for good health and keep them producing well by incorporating basic organic methods to make sure your plants have good air circulation (a few feet between them), good soil drainage, and full sun.