The global economy is still reeling from the impact of the COVID-19 pandemic, and few industries have seen greater disruptions that the airline sector. With so many limitations on travel and the high costs of keeping planes safe for passengers and crew, United Airlines Holdings (UAL -1.27%) fell by more than 75% between January and mid-May.

Since then, though, United Airlines bulls have gotten a lot happier, and the share price has nearly doubled in just the past couple of months. Yet there's still plenty of uncertainty ahead for the company. Long-time investors will remember that United has had to resort to bankruptcy protection in the past, and as much as it's trying to avoid that fate this time around, there are factors beyond its control. Here's what United needs in order to keep itself in the air -- and keep shareholders enjoying a recovery in the airline stock.

1. Travel trends need to keep improving -- and not fall prey to a second wave

The first step for United on its way to a full recovery is for travelers to start booking flights again. The industry have started to see passenger counts bounce back in recent months, with average throughput at security checkpoints across the U.S. rising from less than 100,000 per day in April to more than 750,000 on July 12. That's a far cry from the nearly 2.7 million passengers at airports the same time last year, but it's still a huge amount of progress that has helped restore some confidence in United and its peers.

White and blue jet aircraft with United markings flying at high altitude among clouds, with views of the ground.

Image source: United.

Unfortunately, COVID-19 case counts are up dramatically in the U.S. in recent weeks. That has United and others worried about another long delay in restoring confidence among passengers, especially given that some state governments are imposing quarantine restrictions on those flying from areas that have seen dramatic increases in coronavirus outbreaks. If airline ticket buyers start feeling unsafe again, then they could stop flying and send United into a second tailspin from which it might not recover.

2. United needs not to sacrifice safety for cost-cutting

Building on that theme, United and its peers are under huge pressure to bring in as much in sales as possible while reducing costs to preserve capital. Financing has become expensive, and government assistance will only go so far.

However, United has to balance its desire to stem losses with its need to keep customers happy. For instance, United and American Airlines Group (AAL -0.71%) have been selling middle seats in an effort to boost capacity, rather than leaving them open to encourage greater distancing between passengers. By contrast, Delta Air Lines (DAL -1.45%) and Southwest Airlines (LUV -0.32%) extended empty middle-seat policies through the end of September. By bucking the trend, United is gambling that travelers won't mind middle seats in the middle of a pandemic. That's a risky move, especially with some competitors willing to forego that extra revenue to demonstrate their commitment to customers.

3. United has to find the right size

United is already setting the stage for dramatic workforce reductions. Although it can't impose layoffs until the end of September under the terms of the government assistance packages it received, United has already informed investors that it will cut thousands of administrative and management jobs in October. Crew furloughs could follow, especially if United can't get enough of its professionals to accept voluntary retirement packages.

United will also face the challenge of figuring out how to handle its fleet as it tries to anticipate what travel volume will look like years down the road. That'll be tough for the cash-strapped airline to handle, although it can expect aircraft manufacturers to offer generous terms to keep orders on the books. Whatever United can do to keep its options open as long as possible will help it in its recovery.

Holding altitude

United faces many of the same questions that every airline does right now, and there's only so much it can do to put itself in position to survive and thrive after the worst of the pandemic is behind us. If it can't figure out these three issues well, then the significant gains that the airline stock has enjoyed recently could reverse themselves once again.