The purpose of this study is evaluate if abatacept is effective and safe in decreasing the level of protein loss in the urine in patients with excessive loss of protein in the urine (nephrotic syndrome) due to either focal segmental glomerulosclerosis (FSGS) or minimal change disease (MCD). Candidates must have a prior kidney biopsy with either diagnosis. Another kidney biopsy will not be required as part of the study. Candidates must have failed or be intolerant of prior therapy for their kidney disease. The failed or intolerant therapy must include corticosteroids and at least one other drug. Candidates can be adults and children over the age of 6. Abatacept will be administered by venous infusion every 4 weeks.