BANGKOK, July 19 (Reuters) - The leader of Thailand's election-winning Move Forward Party was braced for what could be his final shot at becoming prime minister on Wednesday, as a parliament that denied him last week convenes for its second vote on the premiership.

Thailand has been run by a caretaker administration since March and 65 days have passed since Move Forward's stunning election triumph over parties backed by the royalist military after nine years of government controlled by generals.

The 42-year-old, U.S.-educated liberal Pita Limjaroenrat needs the backing of more than half of the bicameral parliament to be endorsed as Thailand's next prime minister, but must overcome fierce resistance from a military at odds with his party's anti-establishment ambitions.

Parliamentary rules written by the military after a 2014 coup and skewed in its favour ensured Pita's defeat in the first round, when he was stopped by a Senate appointed by generals allied with conservatives and old money families that have long wielded influence over Thailand's democracy.

Pita has a mountain to climb and knows that if he fails this time, he must honour his pledge to make way for coalition partner and political heavyweight Pheu Thai to field its prime ministerial candidate in the next round.

"I didn't fail. I won the election and formed a coalition and was blocked by the Senate. Let us be clear on that," Pita told Reuters in an interview on Tuesday.

He was 51 votes short and was backed by only 13 of the 249 senators, many of whom abstained or were no-shows, effectively votes against him.