Government Shutdown Prevention Act of 2019 This bill provides continuing appropriations to prevent a government shutdown if any appropriations measure for a fiscal year has not been enacted before the fiscal year begins or a joint resolution making continuing appropriations is not in effect. For an initial 90-day period, the bill provides continuing appropriations at 99% of the rate for the preceding year to continue programs, projects, and activities for which funds were provided in the preceding fiscal year. The bill reduces the continuing appropriations by 1% after the first 90-day period and by an additional 1% for each subsequent 90-day period until the applicable appropriations legislation is enacted.