Toddler's Diarrhea: This condition is common in infants around this age and is characterized by chronic, non-bloody diarrhea with mucus, often without other symptoms like anorexia or lethargy. The absence of systemic symptoms and the age of the child make this a likely diagnosis.

Viral Gastroenteritis: Although the duration is a bit long for typical viral gastroenteritis, some viruses can cause prolonged symptoms. The presence of diarrhea and mucus without blood or significant systemic illness could still point towards a viral etiology.
Lactose Intolerance: This could be a consideration, especially if the infant has recently started consuming lactose-containing products or if there has been an increase in lactose intake. However, it's less common in exclusively breastfed infants.
Food Allergy or Intolerance: An allergy or intolerance to a specific food component could cause chronic diarrhea. Common culprits include cow's milk protein, soy, or, in older infants, other foods.

Infectious Causes (e.g., Giardiasis, Bacterial Infections): While less likely given the clinical presentation, infectious causes can be serious and require specific treatment. Giardiasis, for example, can cause chronic diarrhea and is a consideration in infants with prolonged symptoms.
Inflammatory Bowel Disease (IBD): Although rare in infants, IBD (including Crohn's disease and ulcerative colitis) can present with chronic diarrhea and should be considered, especially if there are other symptoms like blood in stool, weight loss, or failure to thrive.
Intussusception: Typically presents with intermittent abdominal pain and currant jelly stool, but can sometimes cause chronic diarrhea if the intussusception is partial or intermittent.

Congenital Anomalies (e.g., Hirschsprung's Disease): Usually diagnosed earlier in life, but could be a consideration in an infant with chronic, unexplained diarrhea, especially if there are other symptoms like abdominal distension.
Immunodeficiency: Conditions like severe combined immunodeficiency (SCID) can present with recurrent or chronic infections, including gastrointestinal infections leading to diarrhea.
Cystic Fibrosis: Can cause malabsorption leading to chronic diarrhea, but typically accompanied by other symptoms like respiratory issues or failure to thrive.