As far as I understand, the Maharal explains that variations of the number four are used when describing Beitar (four hundred shuls, four hundred teachers of Torah to children, etc.) because the number four indicates importance and solid grounding. Just as a square has four sides that are in each direction and closed in (and a person is considered to have four cubits around him regarding Techum, Kinyan, etc.) so too Beitar was an example of solid achievement and importance in all directions and aspects of spirituality. [He also says that there is a much deeper explanation.]

All the best,

Yaakov Montrose