Do stretch denim jeans get looser after washing?
Eventually, yes. However, they can even shrink after the first wash. It all depends on the fabric profile. The more cotton (denim) in your jeans, the less you should wash them. Fibers like polyester and rayon hold up better to repeated washing.
Trade knowledge suggests three principles: wash your jeans sparingly, hang-dry them when possible, and wash only with cold water. Check out Levi’s recommendations (see the link listed under "Sources") for how to make your jeans last.