There are a lot of factors involved in fabric durability. Generally speaking in terms of material, you want all-polyester or all-nylon fabric. However, also generally speaking, you would find yourself doing well to avoid consumer brands. Consumer brand products are designed for consume needs, such as fashion, low cost, short life, high turnover, etc.
It is better, in general, to stick to clothes designed for commercial applications and, more so, industrial washing. Several companies make industrial/commercial clothing- one of the best known (although so far as I know, they don’t do t-shirts) is Red Kap. Gildan, Eagle Work Clothes, Softwear, Hanes, and Fruit of the loom all make this kind of clothing, too- but it is generally not available through ordinary retail stores.
These are clothes designed by accountants. They are intended to provide the best possible cost equation to a company that provides uniforms on a lease basis. That means that they must cost the least amount of money over time, so initial cost is weighed, but so is how long it lasts. A $10 shirt that lasts 20 washings is not as good as a $15 shirt that lasts 200. (300, btw, is standard wash cycle life for an industrial work shirt, or if you wear it once a week, it should last 5.7 years.)
Durability is depend on printing methods. Transfer Paper will has fast life cycle than screen printing and plate press. The best method is Direct-To-garment printing, this method will spray printing inks directly to your cotton shirt and absorb perfectly to cotton. You can expect it lasting for years. Surely washing methods also affected to life cycle. Please consider to always wash inside out with normal temperature water unless it state different. Read your tag shirts.