Normal variant: Frequent eye blinking can be a normal reflex in infants, especially when they are trying to focus on an object or are exposed to bright lights. At 2 months, infants are beginning to discover their surroundings, and their blinking could be part of their learning and adaptation process.

Dry eyes or irritation: Infants can experience dry eyes or irritation due to environmental factors, which might cause them to blink more frequently.
Allergies: Allergic reactions can lead to itchy, watery eyes, prompting more blinking.
Infection: Conjunctivitis or other eye infections could cause discomfort, leading to increased blinking.

Glaucoma: Although rare in infants, glaucoma can cause eye pain, leading to frequent blinking. It's crucial to diagnose and treat glaucoma early to prevent vision loss.
Corneal abrasion or foreign body: These conditions can cause significant discomfort and lead to increased blinking. Prompt diagnosis and treatment are necessary to prevent complications.
Neurological conditions: Certain neurological disorders can manifest with abnormal blinking patterns. While less common, these conditions are critical to identify for appropriate management.

Blepharospasm: A rare condition characterized by involuntary blinking or spasms of the eyelids. It can be a sign of an underlying neurological issue.
Tourette's syndrome: Although extremely rare at 2 months, Tourette's syndrome can involve motor and vocal tics, including blinking.
Other ocular or systemic diseases: Various rare conditions can affect the eyes or overall health of an infant, potentially causing frequent blinking. These would require a comprehensive evaluation to diagnose.