An improving job market has not helped Wal-Mart Stores Inc.’s (NYSE: WMT) sales. Bill Simon, CEO of Walmart U.S., made that observation to Reuters. What he did not say is where those customers are going. Ultimately that is Walmart’s real problem in its home market.

The comment could mean only one of two things. First, the jobs recovery has hidden a lack of consumer spending. If so, second-quarter gross domestic product (GDP) will be weaker than expected, although not likely a drop of 2.9%, which was posted for the first quarter. Walmart rivals that include, in particular, Target Corp. (NYSE: TGT) and the twin retailers that make up Sears Holdings Corp. (NASDAQ: SHLD) — Kmart and Sears — will suffer badly as well, if the economy is the cause.

On the other hand, Walmart may be losing its place as the largest retailer in America by far. It would take years if not decades for Walmart to fall from the top spot. However, in the meantime, its same-store sales would inch down point by point as the behemoth’s shoppers go elsewhere.

A drop in Walmart’s sales due to the economy can be solved by a rebound. A drop due to customer market share attrition becomes much harder puzzle to address.

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One hint that the trouble is Walmart’s alone is that its same-store sales in the United States have been dipping for several quarters. Some analysts believe that too many rivals offer competing low prices. Some argue that Walmart is really a regional retailer with its markets share concentrated mostly in the central United States. Others reason that Walmart’s inability to enter large cities has hurt it. Likely the most often mentioned reason is that Amazon.com Inc. (NASDAQ: AMZN) has robbed Walmart of enough business to curtail its growth, even if just a little.

Walmart has fought mightily to maintain customers via low-priced pharmacies, quasi-bank operations, a large Web presence of its own and better-targeted discounts. Outsiders say this is not enough. Walmart’s battle with employees over wages has hurt its image just enough to drive a modest number of customers away. Perhaps workers do not even shop at their own employer.

Inside Walmart’s headquarters, a group of senior executives know why Walmart sales have struggled in America. They won’t tell. The answer might reveal that some portion of the problem is close to irreversible.

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