Generally such wounds that do not heal are called non-
healing ulcers in medical term. They could be non
healing due to underlying infection, low supply of oxygen to the wound that is reducing the healing process, underlying diabetes, or due to underlying dermatitis. Wounds heal slower in smokers or alcoholics who have been drinking for a long time. So these have to be ruled out.
Also diabetes leads peripheral neuropathy, atherosclerosis etc which make wound healing troublesome.