Iran Sanctions Preservation Act This bill restricts the authority of the President to waive U.S. sanctions on Iran. Specifically, the bill repeals the President's authority to waive sanctions on the purchase of Iranian petroleum or petroleum products or license otherwise sanctionable conduct concerning such purchases. Furthermore, the President may not remove any Iranian person (including a financial institution) from a list of persons, organizations, and entities that have U.S. sanctions levied against them without certifying to Congress that the person has not engaged in particular conduct, such as supporting terrorism or Iran's nuclear weapons program. In addition, the bill prohibits the removal of the Central Bank of Iran from this list unless there is a Senate-approved treaty between the United States and Iran that addresses Iran's nuclear proliferation, ballistic missile program, and support for terrorism. The President must also maintain Iran's designation as a jurisdiction of money laundering concern until certifying to Congress that Iran is not engaged in illicit financial activities, nuclear proliferation activities, or ballistic missile development. The provisions of this bill terminate on the date the Senate approves a treaty between the United States and Iran that addresses Iran's nuclear proliferation, ballistic missile program, and support for terrorism.