Preserving Taxpayers' Rights Act This bill amends the Internal Revenue Code to establish new procedures and requirements for administrative appeals of Internal Revenue Service (IRS) deficiency determinations. If the IRS determines that there is a deficiency with respect to a tax imposed, it may send a notice of deficiency to a taxpayer after: the taxpayer has been issued a letter of proposed deficiency that explains the basis for the determination of deficiency and provides an opportunity for administrative review in the IRS Office of Appeals; and either: (1) the time provided in the letter for requesting administrative review in the office has expired and the taxpayer has not made such a request, or (2) the office has officially concluded the administrative review process with respect to the deficiency. The bill includes exceptions to these requirements for frivolous tax positions and issues in cases designated for litigation. The IRS must permit a taxpayer to appeal a deficiency prior to issuing a deficiency notice if 60 or fewer days remain on the statute of limitations and the taxpayer agrees to extend the period for 12 months. The bill modifies appeals dispute resolution procedures. It also restricts the authority of the IRS to: (1) designate cases for litigation without permitting an appeal, or (2) offer settlement agreements that preclude an appeal. The bill modifies the authority of the IRS to issue a summons and limits the access that people outside of the IRS have to returns and return information acquired by a summons.