Joshi, who shared the lead on the opening day, slipped down the leaderboard to tied seventh place at five-under 137 after 36 holes.
Meanwhile, the other two Indians Himmat Rai (72-74) and Feroze Garewal (75-78) missed the halfway cut.
Joshi bogeyed first, fourth and 10th and was still three-over when birdied last two holes for a decent finish and keep himself in the race for the title.
Jordan Sherratt of Australia birdied his closing two holes for a five-under-par 67 to seize a two-shot lead at the halfway stage of the Taifong Open on Friday.
Local teenager Lee Chieh-po fired a 68 to share second place alongside countryman Lin Wen-tang (70), a six-time Asian Tour winner, and Thailand's Pijit Petchkasem (67) at the Taifong Golf Club.
Playing in his second year at the Taifong Open, Sherratt took advantage of his familiarity on the course as he put himself in prime position to challenge for the title. He was two-under for the day after 11 holes but shifted into fifth gear when he birdied 11, 12, 17 and 18.
The ADT has announced a provisional 2015 schedule of a minimum 24 tournaments with several more to be announced in due course.
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