What happens is that when you breed birds together that are genetically alike, you end up with inbreeding depression. This can result in a lack of vigor and health in birds, lack of hatchability, genetic deformities, etc. Inbreeding depression can take a few generations of inbreeding to become serious enough so inbreeding for a couple of generations and then adding some new blood is completely fine. When you introduce some new blood, you get the opposite of inbreeding depression-hybrid vigor. Hybrid vigor does not necessarily require crossing birds with a new breed, just adding blood from genetically dissimilar birds(far off cousins or unrelated strains of the same breed and variety, etc) Hybrid vigor results in birds that are healthier, more vigorous, results in better hatchability, and helps keep genetic deformities to a minimum.
When breeding birds, you just need to have a healthy balance of inbreeding and adding new blood. Just know that you need to add some new blood when your birds stop thriving and start to die more easily, have three heads or four feet(just kidding about the three heads, but four feet is not unheard of) and fewer eggs hatch.