Shares of Facebook (Nasdaq: FB), the No. 1 social network, set new lows Tuesday after opening up about 2 percent. Near the close, Facebook shares kept falling about 4 percent to a new low of $25.75, down $1.15. They closed at $25.87, down $1.03 or 3.8 percent.

Since the May 17 initial public offering, Facebook shares have plunged 32 percent. The market capitalization of the company has fallen to only $55.3 billion from $104 billion.

In early activity, Facebook rose to $27.45, up 54 cents. After the first hour, shares gave back most of their gains but stayed up a nickel at $26.95. Then they resumed their decline.

No new analyst forecasts were published early Tuesday. But a new poll taken by Reuters Ipsos found that 34 percent of Facebook users said they're spending less time on the site than six months ago, while only 20 percent they were using it more. That could foreshadow more declines in revenue growth as well as in net income.

Monday's slump came after the influential research firm Bernstein started coverage with an underperform rating for the stock. On Tuesday, more class-action lawsuits against the company were filed, adding to dozens filed in various federal courts in New York and California.

Bernstein suggested a target price of only $25. Analyst Carlos Kirjner projected 2013 Facebook revenue of only $6.4 bilion, about $100 million shy of the consensus, because advertising growth will rise only 38 percent this year and 32 percent in 2013.

On Friday, Facebook shares fell 7.5 percent.

Facebook's continued fall came despite reports it may be near a settlement with Yahoo (Nasdaq: YHOO), the No. 3 search engine, over patent litigation, as well as that might start to offer service to members under 13. That would allow it to keep expanding its membership from the 901 million reported as of March 31.

Other social-networking stocks fell Monday, including Zynga (Nasdaq: ZNGA), the game site that relies upon Facebook. Its shares fell 5 percent to $5.71, and Jive Software (Nasdaq: JIVE), the business social networking site, whose shares fell 4.4 percent to $14.74. On Tuesday, Zynga shares rose 2 cents while Jive's rocketed $1.38, or 9.3 percent.

Facebook, of Menlo Park, Calif., was priced at $38 by its underwriters led by Morgan Stanley (NYSE: MS).

The value of CEO Mark Zuckerberg's personal stake has plunged from $19 billion to only $13 billion.

Facebook, though, raised $16 billion in its IPO.

Bernstein, a unit of Alliance Capital Management, provides research only to Wall Street investors and is well-regarded because it doesn't engage in other activities such as underwriting and banking.

Morgan Stanley rose 50 cents or 4 percent to $12.86 on Tuesday.