TOKYO — Amid tensions over trade and North Korea, Prime Minister Shinzo Abe of Japan leaves Tuesday to visit President Trump at his Palm Beach estate. It kicks off a frenzy of diplomacy that has Mr. Abe meeting President Xi Jinping in China later this year and possibly even North Korea’s Kim Jong-un as well.

Yet Mr. Abe may not stay in power long enough to complete the diplomatic trifecta.

Continuing leaks about a pair of domestic scandals that have dogged Mr. Abe for more than a year are starting to damage his political standing, with a swelling number of voices saying he will not reach his ambition to be the country’s longest-serving prime minister.

Junichiro Koizumi, one of Mr. Abe’s best-known predecessors, told a reporter for the magazine Weekly Asahi that “the situation is getting dangerous” for Mr. Abe and questioned whether the prime minister might resign when the current session of Parliament ends in June.

Over the weekend, tens of thousands of protesters gathered in front of Parliament calling for Mr. Abe to step down, while polls emerged showing that approval ratings for his cabinet had dropped to 37 percent after briefly rallying last week. One poll put it under 27 percent.