What causes under the eye to twitch nonstop for weeks?

Blepherospasm: Botox can help calm that down. See a doctor that gives Botox injections. Sometimes it is from nerves such as a nervous tick.

Several things: Those annoying little twitches under the eye are what's referred to as "myokymia", which is due to irritability of the individual muscle fibers of the orbicularis muscle. These are typically due to sleep deprivation, caffeine, and stress, and are very common. Blepharospasm, a much less common condition, is when involuntary contraction of the muscle that closes the eye causes the eyelid to shut.