Dehydration: Given the patient's age and history of dementia, dehydration is a common and likely cause of dizziness and loss of appetite. Elderly patients with dementia may have difficulty communicating their needs, including thirst, and may not drink enough fluids.

Medication Side Effects: The patient's medications, especially those used to treat dementia, can cause dizziness and loss of appetite as side effects.
Urinary Tract Infection (UTI): UTIs are common in elderly patients, especially those with dementia, and can cause symptoms such as dizziness, loss of appetite, and confusion.
Constipation: Constipation is a common issue in elderly patients and can cause abdominal discomfort, leading to loss of appetite and potentially contributing to dizziness.

Infection (e.g., Pneumonia): Infections can present atypically in elderly patients, with symptoms such as dizziness and loss of appetite rather than the typical fever and cough.
Cardiac Conditions (e.g., Heart Failure, Arrhythmias): Cardiac issues can cause dizziness due to decreased cardiac output or arrhythmias and should be considered, especially if there's a history of heart disease.
Electrolyte Imbalance: Conditions like hypernatremia or hyponatremia can cause dizziness and altered mental status, including in patients with dementia.

Vitamin B12 Deficiency: While less common, a vitamin B12 deficiency can cause neurological symptoms, including dizziness and loss of appetite, especially in elderly patients with poor dietary intake.
Thyroid Disorders: Both hypothyroidism and hyperthyroidism can cause dizziness and changes in appetite, though these are less likely without other specific symptoms such as weight changes or skin changes.