Atopic Dermatitis (Eczema): This is a common condition in infants, characterized by itchy, inflamed skin. The chronic nature of the rash and the age of the child make atopic dermatitis a likely diagnosis.

Seborrheic Dermatitis: A skin condition causing scaly patches, red skin, and stubborn dandruff due to an oily scalp. It's common in infants and can present as a rash.
Contact Dermatitis: This occurs when the skin comes into contact with an irritant or allergen, causing a reaction. Given the duration, it's possible the infant has been exposed to something causing a prolonged reaction.
Impetigo: A highly contagious skin infection that causes red sores on the face, especially around a child's nose and mouth, though it can spread to other areas of the body via touch, clothing, and other items that come into contact with the sores.

Congenital Syphilis: Although less common, congenital syphilis can cause a rash in infants. It's crucial to consider this diagnosis due to its severe implications if left untreated.
Meningococcemia: This is a severe infection that can cause a rash. It's life-threatening and requires immediate medical attention.
Child Abuse (as a cause of skin lesions): It's essential to consider non-accidental injury as a potential cause of skin lesions or rashes, especially if the pattern or history is suspicious.

Staphylococcal Scalded Skin Syndrome (SSSS): A rare but serious condition caused by staphylococcal toxins that typically affects infants and young children, causing widespread blistering and peeling of the skin.
Langerhans Cell Histiocytosis: A rare disorder in which the body accumulates too many immature Langerhans cells, part of the immune system. Skin rashes can be one of the symptoms.
Incontinentia Pigmenti: A rare genetic disorder that affects the skin, hair, teeth, nails, and central nervous system. It can cause a rash that evolves over time.