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Private businesses are key to the economic and social well being of China since they contribute to 90% of new jobs and 70% of technological innovation and new products, according to state news agency Xinhua. And for a country controlled by a single party, maintaining social stability is key.

Since China's largest banks are owned by the state, they prefer to lend to other state-owned companies. That leaves most private businesses with less-transparent channels of financing. Beijing cracked down on that financing early last year as part of an attempt to rein in ballooning untracked debt.

Even before then, smaller companies had a tough time. Small and medium-sized enterprises in China have an average lifespan of 2.9 years, versus seven years in the U.S. and 12 years in Japan, according to a report from The Boston Consulting Group.

Gatley also pointed out that a greater percentage of publicly listed not-state-owned companies in China derive their profits from overseas, making them more vulnerable to rising trade tensions with the U.S.

As growth slowed, the government announced major cuts in taxes and fees, and directed banks multiple times to lend more to private enterprises, especially small businesses.

Some of those efforts have paid off. Analysis from Gavekal showed cash flows from financing for private firms picked up in the first quarter of this year after nearing zero in the fourth quarter of last year.

However, opening the financing spigots — whether from banks or private firms — doesn't necessarily translate into a sustainable turnaround in growth.

Given a lack of reliable credit information, financial institutions still have a difficult time determining which businesses are worth lending to, said Duo Yuan, founder of Beijing-based Bluestone Asset Management.

"China's credit market is far from mature, and some private enterprises, after getting capital from the private funds, play tricks and try not to pay their debts to investors, even when they have the money," he said in an English-language statement. "And due to the absence of legislation in this area, these companies are not even fined or punished. The consequence is that fewer financial institutions dare to buy bonds issued from private enterprises."

Incidents involving two companies in the last several weeks have highlighted the shortcomings of Chinese governance.

In late April, drugmaker Kangmei Pharmaceutical 518-SZ said an "accounting error" resulted in an overstatement of cash in 2017 by 29.94 billion yuan ($4.4 billion). On May 20, the company also disclosed it transferred nearly 8.9 billion yuan to related entities to trade its own shares. Kangmei is a member of MSCI's China Index, as of last summer's review. It's yet to be seen what punitive action regulators might take beyond delisting the stock.

Also in late April, Kangde Xin Composite Material Group said in its first quarter report there was no trace of 12.21 billion yuan the company claimed to hold in a bank deposit. Earlier in the year, the company missed interests payments and defaulted on debt. Local police have taken action against the company's controller, Caixin reported in mid-May , citing a vaguely worded post on Weibo, China's version of Twitter.

Bluestone's Duo noted that longstanding concerns about the ability of investors to recover their money from private enterprises based in northeastern China — so much so that there is a saying in Chinese that "investments must not go beyond Shanhaiguan." The phrase refers to a major Great Wall pass east of Beijing.

Last week, the Shenzhen Stock Exchange disclosed on its website that its department overseeing small and medium-sized listings issued an inquiry into the 2018 annual report of Zhangzidao, a fishery company located in the northeastern city of Dalian.

The company has raised eyebrows in the last few years for blaming massive financial losses on missing or dead scallops. Zhangzidao has until Wednesday to respond, according to the filing. Company representatives did not immediately respond to a CNBC request for comment.

"The fraud risk remains huge in the Chinese market," Gatley said. "(There's) outright criminality at one end, and then firms doing things that don't seem to be business."

"There are large and very difficult vulnerabilities beneath the surface," he added.

On the side of the banks, government requirements for lending to private enterprises could also introduce more risk into the system.

"I actually think banks shouldn't be told to lend to a particular sector, private or (state-owned enterprises)," Weijian Shan, CEO and managing partner at investment firm PAG, said in an email. "Banks should make their own credit decisions based on the creditworthiness of the borrowers. With the risk management systems in place in Chinese banks since the banking reform of early 2000s, they aren't likely to meet policy targets designed to support borrowers of weak credit anyway, which isn't a bad thing."

Shan added that he expects if a company has a reasonable credit record, it shouldn't have trouble obtaining financing.

China is still one of the fastest-growing economies in the world, and analysts see opportunities in areas such as the country's smaller cities. China's official (although frequently doubted)  gross domestic product grew by 6.4% in the first quarter , unchanged from the prior quarter but down from 6.8% a year ago. Authorities project slower growth of 6% to 6.5% this year.

With a state-controlled economy like China's, authorities have shown they can engineer a recovery. The question, for Gatley, is: "After the immediate crisis is past, how (long does Beijing) keep the pressure up?"

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