A recent run of bad news has revived fears that Japan is returning to its familiar role as sick man of the world economy. Its economy shrank in the second quarter and may have done so again in the third, which would qualify as a recession. Inflation has dropped perilously close to zero.

So it might be tempting to write off Abenomics as a failure. That would be a mistake.

Abenomics, the program of radical economic stimulus introduced by Prime Minister Shinzo Abe, has been more successful than many think. Yet that success is fragile, and Japanese leaders have more work ahead to entrench its achievements.

Mr. Abe was elected in 2012 on a platform of three “arrows”: monetary stimulus to defeat deflation, short-term fiscal stimulus coupled with long-term debt reduction, and structural reform to lift Japan’s long-term growth rate.

In early 2013, the Bank of Japan’s new governor, Haruhiko Kuroda, shot the first arrow with massive purchases of government bonds aimed at boosting inflation, then in negative territory, to 2% in two years. The plan was dubbed “quantitative and qualitative easing,” or QQE.

That goal remains far off, but not as far off as implied by the 0.2% inflation rate, which has been held down by falling oil prices. The Bank of Japan’s “core-core” price index, which excludes energy, fresh food and the impact of a consumption-tax increase implemented last year, was up 1.1% in August from a year earlier, the most since 2008. Prices are rising for more products than are falling, and a real-time daily inflation index based on supermarket scanner data is rising at the fastest rate since 2009.

There are also modest signs wages are responding: Unionized workers’ base pay increases were 0.7% in the fiscal year ended in March, the highest rate since the late 1990s.

Japan’s negative growth is not as catastrophic as it sounds. Because of the country’s shrinking labor force and low productivity growth, underlying “potential” growth for the economy is 0.5%, or lower. That means modest shocks such as last year’s tax increase and a slump in exports to China more easily push growth into negative territory, without initiating a genuine cyclical downturn.

A better indicator of underlying economic health is unemployment, which adjusts for a shrinking labor force. It has edged down from 4.1%, when QQE began, to 3.4% now. Unlike in the U.S., this is not because workers are dropping out; the share of Japan’s population over 15 working or looking for work—the participation rate—has edged higher since 2012, largely thanks to a remarkable rise in participation by women and the elderly.

Thanks to modest growth and rising prices, Japan’s nominal gross domestic product—its output of goods and services without adjusting for inflation—has been rising since QQE began, after several decades of stagnation. If nominal GDP keeps growing while interest rates stay near zero, it will vastly ease the burden of Japan’s massive government debt, which now approaches 250% of GDP.

Still, this is hardly a resounding success. Economists Joshua Hausman and Johannes Wieland note that private forecasts of Japanese GDP in coming years are no higher than before Abenomics began. They found no evidence that net debtors and the young, who would be most likely to spend more in response to more stimulative monetary policy, had done so. The weaker yen has not produced the expected boom in Japan’s trade or restrained imports much.

Why hasn’t Abenomics had more bang? Partly, bad luck: China’s slowdown has hit Japanese exports, and falling oil prices have made it harder to persuade business and the public that higher inflation is here to stay. Mr. Abe also bears some blame: Last year’s consumption-tax increase set back growth, and the government has delivered few structural reforms to speed up underlying growth.

That could be about to change. This week’s completion of the Trans-Pacific Partnership signals a greater will by Mr. Abe to take politically unpopular actions to expose inefficient parts of Japan’s economy to greater competition. “It’s time for us to start innovating and step into a new, open world,” Mr. Abe exhorted this week.

But the biggest problem is that even as inflation has turned positive, wages have been slow to follow. A decade of deflation has undermined the practice of firms awarding across-the-board wage boosts each spring. Japanese firms increasingly meet new sales with part-time and temporary workers with fewer protections and lower pay than full-time permanent workers. This erosion of workers’ bargaining leverage has made it harder to get wages rising even in the face of historically low unemployment and buoyant profits, a phenomenon the U.S. has also experienced.

Changing this dynamic is Japan’s biggest challenge. Mr. Abe has pressed firms to deploy more of their cash on salaries and capital expansion and encouraged them to create more permanent jobs. But persuading firms to do so will likely take even lower unemployment, and confidence that growth is not about to evaporate again because of an ill-timed tax increase or a recession in the rest of the world. Mr. Abe can certainly avoid the first; the second is out of his hands.