An organization charged with reviving Miami-Dade’s battered economy finds itself with some bruises, too.

The Beacon Council, a non-profit that relies on tax dollars, is contending with a threat to its public funding, lukewarm support from County Hall and a rift within its own leadership. CEO Frank Nero faces a revolt from some board members, and the full board this month opted not to pass a motion expressing confidence in the Beacon Council’s management, according to several participants.

“Not everybody loves Frank,’’ said Joseph Pallot, the group’s volunteer chairman and general counsel at Heico Corp. But Pallot said Nero has performed well as the head of an organization that receives about $4 million a year in Miami-Dade taxes. “Frank’s economic-development skills are second to none.”

Nero, a former New Jersey municipal leader who earns about $400,000 a year, declined to comment. He has tussled with board members and elected officials in the past. But he now faces pressure on multiple fronts, with Miami-Dade Mayor Carlos Gimenez wanting to revamp the county’s economic-development strategy, commissioners wanting to take away $1 million in tax funding and give it to local businesses, and some Beacon board members pushing for a change at the top.

“We have issues with the Beacon Council,” Gimenez said this week in an interview. “The commission also apparently has issues with the Beacon Council. We’re trying to work with them as best that we can.”

In his comments, Gimenez also said his concern was with the county’s “disjointed” approach to economic development, saying, “I’d like to kind of bring that all together.”

The Beacon Council’s primary mission is to recruit companies to Miami-Dade, serving as a go-between among corporate relocation firms and local agencies and helping line-up incentives and subsidies from county and state pools of money. It also pursues various economic efforts and promotions, including a year-long “One Community One Goal” study of how to grow the economy, and next month’s awards fundraising lunch aboard a cruise ship at Port Miami.

In the budget year that ended in September 2011, the Beacon Council received about $1.6 million from businesses paying dues, events and other private-sector sources, according to the most recent fianancial statement available.

Last year, the Beacon Council said it helped 27 businesses either expand in or move to Miami-Dade, accounting for about 2,000 new jobs. Among the big companies it helped land incentives for was the new cable network Univision is forming with the ABC national network in Doral.

But the Beacon Council’s public dollars have proved a ripe target, with commissioners complaining the money goes to recruit large companies to town that then compete with constituents’ smaller businesses.

Combined, the Beacon Council’s top eight executives make about $1.5 million a year, and during the recession the group spent about $1.5 million on a 2009 renovation of its rented Brickell Avenue office, according to tax filings and financial statement.

“When you’re trying to bring a CEO to Miami, you have to play the part that you’re a cosmopolitan, global city,’’ said Ana Acle-Menendez, head of communications for the Beacon Council. “That was the idea behind the renovation.”