Brain shrinking in medical term known as brain atrophy. It is a normal phenomenon that with increasing age our brain naturally shrinks. But in some diseases like Alzheimer's disease, Parkinson's disease etc brain shrinks abnormally faster even in youth and produce memory problem ,dizziness, walking difficulty. In patients who smokes who take alcohol tobbacoo, those having nutritional deficiency like some vitamin deficiency Brain also shrinks abnormally. Patients of diabetes blood pressure high cholesterol brain also shrinks fast and abnormally. . In your patient dizziness and walking difficulty may be because of brain shrinking. but also look for blood pressure in lying down postion and standing position to look for postural hypotension . More information regarding patients other health status also required to give a definite diagnosis.