Protection of Saudi Dissidents Act of 2019 This bill imposes limits on arms sales to Saudi Arabia and requires various reports and actions related to the death of Saudi Arabian journalist Jamal Khashoggi. The President may not transfer or authorize for export certain defense articles or services to Saudi Arabia's government for 120 days after this bill's enactment. After this period, the prohibition shall remain in effect unless the President periodically certifies to Congress that Saudi Arabia (1) is cooperating with an independent investigation into Khashoggi's death, (2) has released all detained journalists and human rights activists, (3) is protecting its citizens' freedom of religion, (4) is taking verifiable steps to stop torture of detainees, and (5) has disbanded intelligence and security units dedicated to silencing dissidents in other countries. The Department of State shall periodically certify to Congress that individuals with Saudi diplomatic credentials are not using such credentials to track or harass Saudi nationals in the United States. If the State Department does not make such a certification, it shall close at least one Saudi diplomatic or consular facility in the United States until the certification is made. The bill requires reports to Congress on (1) whether any Saudi officials have engaged in a consistent pattern of harassment against any individual in the United States, and (2) whether the intelligence community fulfilled its duty to warn Khashoggi of the threats to his life.