TOKYO (Reuters) - Japanese Prime Minister Shinzo Abe faces criticism over suspected cronyism scandals and cover-ups that are eroding his support and raising doubts about how long he can stay in power.

Japan's Prime Minister Shinzo Abe attends a lower house budget committee session at the parliament in Tokyo, Japan, April 11, 2018. REUTERS/Toru Hanai

Following are factors likely to signal whether Abe, who returned to power for a rare second term in December 2012, will resign or opt not to run in a September ruling Liberal Democratic Party (LDP) leadership race that he needs to win to stay in office.

‘SMOKING GUN’

Abe has repeatedly denied that he or his wife, Akie, directly intervened to get preferential treatment for people he knows. Finding a “smoking gun”, or clear evidence that proves direct involvement by the premier, may prove difficult, experts say, but evidence he had lied in remarks to parliament would be extremely damaging.

A steady drip of revelations that officials acted out of a belief they were carrying out Abe’s wishes would also take a heavy toll if voters decided he bore ultimate responsibility.

SAGGING SUPPORT, ‘AOKI INDEX’

Historically, a sharp slide in a prime minister’s public support to about 20 percent or lower for several months has often proved fatal, especially if an election is near. No general election is scheduled until mid-2019.

Some political experts watch the “Aoki index”, named after a ruling party heavyweight and calculated by adding a premier’s rating to ruling party support. A rating of less than 50 signals trouble. Abe’s index now is 73.4.

But incumbent prime ministers can be stubborn even if ratings slide. Taro Aso, who is now Abe’s finance minister, saw his ratings drop below 10 percent in 2009 but stayed on to lead the LDP to an historic defeat that August. The LDP lost power and Aso lost his job. Abe’s support fell below 30 percent last summer, but he led his coalition to an election win and his ratings have rebounded.

CRITICAL COMMENTS

Comments by LDP power-brokers including Secretary General Toshihiro Nikai suggesting - even if obliquely - that it is time for a change at the top would signal Abe’s days are numbered. So could signs that popular LDP lawmaker Shinjiro Koizumi was backing an Abe rival in a challenge to the premier. Business leaders might also speak out.

Critical remarks by leaders of the LDP’s junior coalition partner, the Komeito party, could also signal danger. It is traditionally more sensitive to scandals than the LDP.

If the ruling bloc agrees to opposition demands that Abe’s wife testify in parliament about her role in one of the suspected scandals, Abe could resign rather than let that happen.

FINANCE MINISTER’S FATE

A decision by Finance Minister Aso to quit over admissions by his ministry that officials altered documents related to the murky land sale at the heart of one scandal would remove one bulwark against direct criticism of Abe. It would also deprive the prime minister of a close ally in the cabinet.

Aso has rejected calls to quit. Whether he would continue to back Abe for a third LDP leadership term if forced to fall on his sword is unclear.

DIPLOMATIC DEVELOPMENTS

Last year, Abe’s support dropped below 30 percent in some surveys over the scandals and the LDP suffered a big loss in a Tokyo assembly poll. But helped by worry about North Korea’s missile and nuclear programs and opposition disarray, Abe led his ruling bloc to a big win in an October snap election. A revival of similar regional security concerns could help Abe again.

Conversely, a poor showing at his meeting with U.S. President Donald Trump next week, when Abe is expected to face pressure on trade, would dent his standing with his party, since Abe has made much of his good relations with Trump.

OSAKA PROSECUTORS

Any arrest of key figures by Osaka public prosecutors, who are investigating the murky land sale to a school operator with ties to Akie Abe, could trigger fresh revelations, further denting Abe’s support.

Former finance ministry official Nobuhisa Sagawa testified in parliament that neither Abe nor Aso had ordered documents to be doctored, or intervened directly in the land sale. But he declined to comment on how or when he knew about the changes, citing concern about a criminal investigation.

HEALTH PROBLEMS

Abe cited health problems when he resigned at the end of his first term as premier, in September 2007, after a plague of scandals in his cabinet, a devastating election loss and a hung parliament.

He takes medication for a chronic ulcerative colitis condition. Speculation periodically emerges that stress could cause a recurrence of the malady.