There are two forms of rejection that can occur with kidney transplantation. The most common is cellular rejection, whereby the immune system attacks the kidney with T-cells and macrophages that can destroy the kidney. This form of rejection is relatively easy to treat and usually responds to increases in immunosuppression (such as an increase in prednisone).
Humeral rejection is less common and results from B-cells being sensitized to attack the kidney with proteins known as antibodies. These antibodies then cause a much slower immune response that is very difficult to treat. Increased immunosuppression, plasmapheresis and B-cell inhibitors are commonly used to treat this disease, but it is very difficult to control and manage. Kidneys are often lost to humeral rejection despite the best treatment available.
Transplant immunology is a very complex area of medicine. I recommend that your son-in-law continue to consult with a transplant nephrologist.