why diabetic patient persist their injury without healing?

case:
Three days ago, Jean Quinn, 43, underwent a bowel resection to relieve an obstruction. She's 5 feet 3 inches, weighs 160 pounds (72.8 kg), smokes, and has steroid-induced, insulin-dependent diabetes. Mrs. Quinn's postoperative course has been relatively uneventful, except for a productive cough.
As you begin evening rounds, you notice that Mrs. Quinn has a low-grade fever, complains of pain at her incision line, and appears sluggish. Although the incision remains intact with staple sutures, you notice redness, swelling, and small amounts of serosanguineous drainage in the center of the suture line. You see that it's been noted by the physician in her chart.

Later that night, Mrs. Quinn calls you because she can feel drainage from the incision site and is experiencing sharp incisional pains. You note that the center of the incision has opened approximately 5 x 4 x 2 cm (2 x 1.6 x 0.8 inches). The wound is pale pink on the inside with small amounts of yellow exudate on its floor. You alert Mrs. Quinn's physician.

Identification

1. is a set of metabolic disorders. Generally the term "diabetes," when used alone, typically refers to diabetes mellitus, which is characterized by sweet urine. This is due to an excess of glucose in the blood, not all of which can be filtered out by the kidneys, leading to some being present in the urine. Diabetes mellitus is due to problems with insulin. 

Types

1. There are two types of diabetes mellitus. The first, type I, is due to an inability of the islet cells in the pancreas to produce insulin. Type II diabetes is marked by resistance to endogenously produced insulin. Since insulin is critical in the the uptake and regulation of glucose in the blood, both types lead to increased blood sugar

      Effect
          Insulin-dependent patients may have trouble because hyperglycemia supports    
          bacteria growth. Also, diabetes slows collagen formation, interfering with wound closure   
          and strength.
 

Prevention/Solution

1. The best way to avoid serious complications is to make sure that diabetics inspect their feet as often as possible. Any sort of foot cut can be treated with a variety of techniques, including the administration of growth factors to try and speed the wound healing response. Removal of diseased and infected tissue can also speed the process. More recently, there has been a movement to inject cells necessary for wound healing directly onto foot ulcerations in diabetics. 

GANGRENE

gangrene is necrosis(dead)  tissue with superadded putrifaction.
putrifaction is cause by saprophytic bacteria which break down the proteins of the necrotic tissue liberating hydrogen sulphide that give the tissue a foul odour.

Hydrogen sulphide unites with the iron of heamoglobin forming iron sulphide that stains the gangrenous tissue black

Diabetic foot ulcers can become infected with gangrene and can result in amputation of the affected limb.