For years, Fang Fenglei was Wall Street’s go-to fixer in China — a partner to heavyweights like Goldman Sachs Group Inc. who built one of Asia’s most prominent private equity firms.

Now, after a stretch of mediocre returns, subdued dealmaking and leadership churn at his Hopu Investment Management Co., even longtime backers such as Temasek Holdings Pte, GIC Pte and China Investment Corp. are rethinking their commitments, according to people familiar with the matter.