Word is that Elevation Partners, the high-profile if poorly timed private-equity firm headlined by rock star Bono and star investor Roger McNamee, is considering raising a new fund.

As surely as dogs chase rabbits or night follows day, PE shops raise more money when the existing fund is mostly used up. (Elevation’s is about 70% invested.) Yet when all you have to show for your first effort are embarrassing misses — no rabbits caught, mostly grim darkness, metaphorically speaking — it’s got to be tough to collect fresh cash.

This is the tough position in which Elevation finds itself. Despite having raised $1.9 billion in 2004, the ballyhooed firm is far from a successful experiment. It’s got all of one exit, a gaming-company sale to Electronic Arts (ERTS), headed by an Elevation co-founder.

Two of its investments are seriously sick. One is the online real estate dog Move.com (MOVE), better known by its scandal-ridden former name, Homestore.com. The other is Forbes Media, the parent for FORTUNE competitor Forbes Magazine, in which Elevation invested at perhaps the worst time in decades for media enterprises.

The snafus sting, of course. But the fate of Elevation’s first fund rests almost solely on one investment, its $460-million stake in beleaguered smartphone maker Palm (PALM). That investment is barely in the money for Elevation. It’s worth about $500 million currently.

Elevation is demonstrably in for the long term: It chose not to sell late last year when the stock peaked around $18, compared to Tuesday’s close of $11.65. Palm recently raised $500 million in a stock offering, so its near term is secure.

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But the company is a long way from a home run, unless Elevation forces a sale to a bigger player like Dell (DELL) or Microsoft (MSFT). Remaining independent is an expensive proposition, however, as Barclays analyst Amir Rozwadowski notes to clients.

“We believe that its improved cash position should enable the company to be very aggressive in its marketing efforts over the next few quarters, particularly as the company looks to improve brand recognition, carrier distribution, and overall awareness of its products,” he writes. “We do however expect the company to continue to burn cash at a healthy clip in the near term, as expanding scale is at the top of management’s agenda.”

Elevation declined to comment on its fundraising agenda. It needs to raise a new fund, though, in part because it recently added longtime eBay CFO Rajiv Dutta to its ranks as managing director. New bigshots typically don’t get to participate in the “economics” of five-year-old funds, so if Dutta, a skilled operations and financial executive, is to make some serious money at Elevation, he’ll need a fund from which to invest.

Elevation doesn’t have trouble getting meetings. Endowment heads are likely to agree to a sit down if Bono shows up. Once in the room, there are few better talkers in Silicon Valley than McNamee. (A wonkish fantasy: a “talk-off” featuring McNamee, venture capitalist John Doerr and Apple’s Steve Jobs. Imagine the possibilities.) McNamee and his partners will have their work cut out for them, though. One win, two disasters, a couple fresh investments and one still risky possibility. Not the strongest lineup to bring into a pitch meeting.