How long does it take to cure strabismus through vision therapy?

It may never cure. Strabismus can occasionally be improved by vision therapy, but more often requires multiple treatments, including glasses and even surgery. Even once the strabismus has improved, it can return years later, especially if the original treatment was begun at an older age, or did not completely treat it.
Variable. Strabismus due to refractive problems will respond quickly but will only appear gone while correction lenses are in place. Length of therapy for amblyopia ( lazy eye) will depend upon the age it is initiated. Vision therapy alone will not straighten eyes. Ophthalmic evaluation is critical to determine the necessary treatment for strabismus.