TOKYO—Japan’s industrial output fell for the second straight month in August as COVID-19 outbreaks elsewhere in Asia disrupted supply chains for carmakers already facing headwinds from a prolonged chip shortage. Separate data out on Thursday showed retail sales in August slipped for the first time in six months as households cut spending amid a coronavirus relapse, signalling lacklustre consumer sentiment. The data suggests the pandemic continued to gnaw at Japan’s economy this quarter, posing an immediate challenge to the next prime minister, Fumio Kishida, who won the ruling party leadership vote on Wednesday, ahead of general elections that must be held by late November. Factory output lost 3.2 percent in August from the previous month, official data showed on Thursday, hit by weaker production of cars and electronic machines and marking the second consecutive month of contraction after a 1.5 percent drop in July. The decline was larger than the …