Why do patients with diabetes mellitus often develop albuminuria?

Kidney disease. People with long-standing diabetes can develop nephropathy, or kidney disease. When the kidneys are functioning properly, there is only tiny amount of a protein called Albumin found in the urine. As the kidney filtering fails in diabetic nephropathy, there will be more and more protein spilled into the urine, causing albuminuria (high amounts of Albumin in the urine).
Damage to kidneys. Albuminuria simply indicates damage to the kidneys, causing protein to spill out in the urine. It's a sign that the diabetes (and blood pressure possibly) need more control.