The drug maker Gilead Sciences Inc. has been remarkably resilient under a barrage of political attacks and public protests about the high prices of its medications.

But in recent weeks it’s hit some bumps: Deaths of patients taking its cancer drug; new competition for its most lucrative product; and now, a loss in a high-stakes patent battle that could cost it billions.

That turbulence has hit Gilead’s stock. But its biggest financial challenge may well be more pedestrian: a declining flow of patients for the company’s blockbuster hepatitis C drugs.

Sold as Sovaldi and Harvoni, the drugs have so far treated about 380,000 people in the United States and about 390,000 elsewhere in the world, according to Gilead spokeswoman Cara Miller.

Last year alone, Sovaldi and Harvoni generated $19.1 billion in sales—nearly two-thirds of Gilead’s total revenue.

That dependence on one class of products is a red flag for investors. “At some point we’ll just run out of patients,’’ said Brian Skorney, a senior research analyst who covers Gilead for the financial services firm Baird. “The biggest question mark on Gilead from an investor’s standpoint isn’t the pricing issues, but . . . how durably are we going to see hep C patients come through the system.’’

To be sure, Gilead has only reached a fraction of the tens of millions of people worldwide with hepatitis C. Miller said the company is “confident in the long-term sustainability’’ of global hepatitis markets. She also pointed to efforts by companies, governments, and patient groups to improve diagnosis rates and access to care.

But Gilead has already treated a not-insignificant chunk of the patients who can be easily reached — and who have the means, either on their own or through insurance, to pay for the drugs. (A full course of treatment with Harvoni goes for $94,500 and with Sovaldi, $84,000, though insurers often negotiate substantial discounts.)

Gilead often can’t charge as much for its hepatitis C drugs overseas; indeed, in many countries, it sells the medications for less than 10 percent of the sticker price in the United States.

While the American market seems large, with more than 3.5 million people infected, there are few new cases of hep C these days. The remaining untreated patients are disproportionately poor, homeless, or incarcerated. And many who have lived with the disease for decades aren’t inclined to seek treatment, either because they were scared off by the bad side effects of older generations of medicines, or they aren’t experiencing troubling symptoms.

Newly-installed chief executive John Milligan told CNBC reporter Meg Tirrell on Wednesday that looking forward, “the big barrier to treating everybody will be identifying them and getting them into treatment.’’

Gilead has said it expects sales from Sovaldi and Harvoni to flatten this year. New US prescriptions of Harvoni, the newer and now more heavily prescribed of the two, have tapered off since peaking last spring, though they recovered somewhat this month, according to estimates from the research firm Symphony Health.

The challenge is especially acute because Sovaldi and Harvoni work so well. Many bestselling drugs that treat chronic diseases must be taken for years or even decades. But the Gilead products can cure hep C in a couple months, and the patient never needs to take them again.

To add to Gilead’s challenges, rival pharmaceutical company Merck got approval this year for its own hepatitis C drug, Zepatier, which competes with Harvoni and starts at a lower sticker price — $54,600 per treatment.

This week a federal jury in Northern California found that Merck’s scientists made some of the key discoveries that led to the development of Gilead’s hepatitis C drugs. Merck has demanded $2 billion in damages plus royalties on the sale of Harvoni and Sovaldi. The jury will decide on penalties.

Leerink analyst Geoffrey Porges said in a note to investors that his firm expects the damage award to be “relatively modest.’’

Another wild card for Gilead: The attorney general of Massachusetts in January threatened to sue the company over the high cost of the hep C drugs, saying its pricing strategy may be an unfair trade practice.

Then there’s Gilead’s blood cancer drug, Zydelig, which is on the market but continues to be tested in clinical trials.

Last week Gilead shut down six of those trials over significant safety concerns, including patient deaths. The Food and Drug Administration issued a warning to health care professionals. Zydelig wasn’t a big revenue source for Gilead. But still, the setback — along with the departure of a key scientist — raises questions about whether the company can move into oncology, as it had planned in a bid to diversify.

Amid a broader slide in the biotech market, Gilead’s stock price has dropped 25 percent since its recent peak in June. It closed Thursday at $91.32, up 1.38 percent. Some investors are clamoring for the company to acquire new drugs, while others want Gilead to stand pat.

“There is nothing more fascinating than being in an investor dinner with two groups pairing off against each other,’’ Milligan said on CNBC on Wednesday. “Sometimes I don’t even have to talk in those meetings.’’

Rebecca Robbins can be reached at rebecca.robbins@statnews.com. Follow her on Twitter @RebeccaDRobbins. Follow Stat on Twitter: @statnews.