Say two parties enter into a professional services contact and the contract is silent as to what constitutes a breach of contract. Then during the performace of the contract the party which is performing the services doesnt deliver the services as required by the contract. If the party receiving the services stops the other party from performing the services and call "breach" and the other party doesnt cure the breach, what, if anything should the parties do to memoralize the agreement? Should they sign a waiver and release of claims or just ignore the rest fo the contact and move on?

They are do either. Breach and walk away or breach and sign mutual releases. I'd opt for the later, especially if it was for my client

If you do nothing then you have to wait out the statute of limitations based on contract law. If releases are signed, then the parties can just move on. Make sure the release recites some form of consideration.