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The Bitcoin frenzy appears to be fading. But an upstart exchange made a big bet last week that the virtual currency still held promise as an investment.

The exchange, SecondMarket, which is based in New York, nearly swept the government’s latest Bitcoin auction, winning 48,000 of the 50,000 Bitcoins for sale. The exchange’s syndicate, which received 104 bids from eight parties, won 19 of the auction’s 20 Bitcoin blocks.

“Obviously, we’re very thrilled with the results,” said Brendan O’Connor, the managing director of trading at SecondMarket. SecondMarket was started in 2004 by Barry E. Silbert, who runs the Bitcoin Investment Trust investment fund.

The venture capitalist Timothy C. Draper, who won all of the nearly 30,000 Bitcoins in the United States Marshals Service’s first auction in June, said last Friday that he had won only 2,000 Bitcoins in last week’s auction. Mr. Draper bid on behalf of his venture firm, Draper Associates.

The Marshals Service confirmed on Tuesday that SecondMarket had won 48,000 Bitcoins and that the transfer of the coins was completed on Monday.

The auction last Thursday of 50,000 Bitcoins, worth about $19 million, was the second by the Marshals Service for Bitcoins seized in connection with Silk Road, the defunct online bazaar. In June, it sold nearly 30,000 Bitcoins seized from Silk Road, which was shut down in October 2013 after the authorities said it was an online marketplace for illegal drugs and other illicit activities.

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A number of other prominent Bitcoin players, including Pantera Capital and Mirror, previously called Vaurum, also participated in last week’s auction.

Still, the latest sale raised questions about whether the appetite for Bitcoin among investors was subsiding.

The Marshals Service said last week that only 11 bidders participated in Thursday’s auction, a sharp decrease from the first auction, when 45 bidders took part. The service received 27 unique bids this time, compared with 63 in June.

And at the time of the second auction, Bitcoin was trading at about $370, down from its peak of about $1,150 a year ago and about $200 below its price at the start of the first auction in June, according to CoinDesk’s Bitcoin Price Index. It was trading just below $350 on Tuesday morning.

“The demand is starting to dry up,” said David L. Yermack, a professor of finance at New York University’s Stern School of Business. “I think a lot of the excitement may have bled out of investors.”

Bitcoin’s wild price fluctuations, which analysts had said were driven partly by speculative trading, have all but disappeared in recent months. This price stability, in turn, might have further discouraged opportunistic, short-term investors from participating in the auction, Mr. Yermack said.

Others in the Bitcoin industry, however, dismissed the notion that the virtual currency was no longer an attractive investment. Instead, they said, the fact that fewer bidders participated in the second auction was a sign that the Bitcoin market was becoming more liquid.

“Volumes have picked up, so there are other ways to get larger trades relatively easily,” said Garrick Hileman, an economic historian at the London School of Economics who studies alternative currencies. “The Bitcoin market has matured.”

The government’s two auctions represent only a small portion of the total amount of Bitcoins seized in connection with Silk Road. The government has recovered 173,991 Bitcoins, including 144,336 found on computer hardware belonging to Ross Ulbricht, who is said to have created Silk Road.

Lynzey Donahue, a spokeswoman for the Marshals Service, said by email at the time the second auction was announced that the agency anticipated selling the remaining Bitcoins “in the coming months,” but that “no exact dates have been determined.”

The promise of at least one more auction, however, has some in the Bitcoin industry worried. “Bitcoin is in a bit of a holding pattern, or a bit of a lull, and people may think that there’s more downward pressure on the price,” said Mr. Hileman, the economic historian. “Now, we’re onto the harsh reality of who wants to buy into another auction.”