There's a growing contradiction at United Continental (UAL -0.08%).

On the one hand, the United Airlines parent company has maintained its commitment to capacity discipline. In the face of weak unit revenue trends, United is holding domestic capacity growth below 2% this year. On the other hand, the company admitted last month that domestic capacity cuts have caused United to lose market share in its hubs over the past five years. It believes this has hurt its unit revenue.

United Airlines has lost market share in the U.S. over the past five years. Image source: The Motley Fool.

This puts CEO Oscar Munoz and his management team in a bind. If United Airlines increases its domestic growth rate, it will worsen the current capacity glut, especially if it provokes a response from any of United's competitors. That would almost certainly drive unit revenue down even further. But if it does nothing, United's market share in its hubs will continue to languish.

There may be only one way out of this dilemma: downsizing or eliminating one or more of United's remaining hubs.

Management recognizes that there is a problem

United Airlines first addressed the issue of losing share in its hub markets on an investor call last month. To halt this trend, the carrier is adding capacity in San Francisco and Denver this year, two markets where demand is particularly strong right now.

However, United's management team also appears to realize that pivoting to aggressive growth across the entire route network would not be wise. On the June investor call and again on the company's recent Q2 earnings call, Munoz talked about needing to "refine the mission for each geographic region, hub, and spoke."

United's dilemma is further complicated by the company's move to "upgauge" its domestic fleet, following in the footsteps of Delta Air Lines (DAL -0.58%). As part of this initiative, United will cut its fleet of 50-seat regional jets from more than 250 planes today to fewer than 100 by the end of 2019. They will be replaced by mainline planes in the 120- to 130-seat range.

This will force United to either dramatically increase capacity in certain markets (undermining unit revenue) or cut flight frequencies (which could drive away business travelers).

United Airlines will retire most of its 50-seat jets by the end of 2019. Image source: The Motley Fool.

A few years ago, Delta squared this circle by closing its hub in Memphis and gutting its hub in Cincinnati (which now has fewer than 100 daily flights, down from about 600 a decade ago). This allowed Delta to add larger planes to its fleet and use them to connect traffic through its big hubs in Atlanta and Detroit, rather than splitting that connecting traffic among four hubs.

Two hubs are in danger

United already closed its Cleveland hub in 2014, after years of weak performance. Considering that it already had three larger hubs within 400 miles of Cleveland, this was an obvious move.

However, two more United hubs could potentially be on the chopping block: Los Angeles and Washington, D.C. Not coincidentally, those are its only two hub markets where United doesn't hold the No. 1 position in terms of seat share.

In Los Angeles, United faces brutal competition from virtually every major airline. Meanwhile, less than 350 miles away, it operates the premiere West Coast airline hub in San Francisco.

Rather than fighting a losing battle in LA, it might be wiser for United to shrink significantly there. It can funnel connecting traffic through San Francisco and it even might be able to retain local customers in LA by offering frequent flights to its other hubs. Delta Air Lines has the best margins in the industry despite having no hub in Chicago, suggesting that there's no strategic imperative forcing United to have a hub in every top-tier market.

Meanwhile, United's hub at Washington Dulles International Airport is barely more than 200 miles from the carrier's larger and far more profitable Newark hub. United Airlines is in a particularly tough spot in Washington, D.C., because most travelers vastly prefer to fly from Reagan National Airport, which is closer to the city center.

Furthermore, the FAA is removing Newark International Airport's slot constraints as of this fall. This would allow United to start adding flights there if it wants to -- something that hasn't been an option recently (at least on peak days).

Rather than fighting at a disadvantage against American Airlines, which has a hub at Reagan Airport, United might be better off downsizing in Washington, D.C., while growing at Newark Airport.

Decisions coming later this year?

United Continental is still trying to work through its long-term network strategy. But United will hold a full investor day conference during the fourth quarter where it will spell out its plans in more detail. There's a good chance that downsizing -- or even closing -- the Los Angeles and Washington, D.C., hubs will be on the agenda.