My response:
Well, I checked PA law, and it appears that PA does, in fact, allow contractual Liquidated Damages clauses, as opposed to States like Delaware and Colorado. Liquidated Damages is a sum of money agreed upon by the parties to a contract that will be paid as damages if there is a breach of the contract. In this case, you signed a contract, and have decided not to fulfill your obligations thereunder - - a breach of the contract.
Liquidated Damages is a specified amount of money provided for in a contract as compensation if the contract isn't fulfilled. For example, an offer to buy property may include a provision that once the seller accepts the offer, the seller may keep the buyer's deposit as liquidated damages if the buyer doesn't complete the purchase. Liquidated damages may be used only if the damages expected as a result of a breach of contract are uncertain or difficult to prove and the amount given as liquidated damages is reasonable.
In this case, the school does not know the full extent of its damages if someone, like yourself, refuses to pay the agreed tuition. In the meantime, the school has a limited amount of seats to fill, and may, in the meantime, have turned away other parents applying for their children because you "reserved" a seat for your child. Prior to your breach of the contract, the school had an obligation to you to make sure that a seat was available for your child.
With less time available, the school is now required to "scramble" to try and fill that seat, costing them money in the process that they wouldn't have otherwise needed to spend.
Since you signed the contract, and you are the breaching party, you're stuck.
IAAL