If most Filipinos trust the U.S. more than they trust China, this could certainly hurt Duterte's support because the U.S. does not agree at all with President Duterte's policies and his way of doing things in a way that is seen as inhumane in the U.S. Filipinos can sense this and their loyalties might be thwarted.
91% (of the most vocal and available to be surveyed) in a trust rating doesn't mean that 100% of them approve of what he is doing. There's a big difference between being asked if you trust that man and being asked if you approve of that man killing anyone that doesn't conform to his laws exactly as he wants them to or his crazy idea about leaving the UN that would've isolated this country and send us into a recession.
Duterte has said some things that paint the US in a bad light. These things are sure to lower his support. Also, the United States and many of its citizens have criticized Duterte for some of the things he has said and done in the past. Incluíding his remarks about criminals.
Philippine President Duterte's support will be hurt by a recent poll showing his citizens trust the United States the most. Duterte has increased his anti-American rhetoric and has indicated he will drop joint military exercises, which flies against the beliefs of his own citizens. At the same time, these citizens trust China the least.