Mario Gabelli’s decades-long frustration with United States Cellular Corp. may be reaching a new high.

The legendary investor has been the leading outside shareholder in the family-controlled cellular operator for years and, despite eroding revenue and a falling stock price, cannot get the Carlson family to put the business up for sale.

That’s even though Gabelli is convinced the Chicago-based wireless company — the largest regional carrier in the country — can fetch nearly twice its current stock price, a source with close knowledge of his thinking said.

The company’s shares closed Friday at $37.56. The stock is down 14 percent this year and 18 percent over the last 12 months.

US Cellular’s 5 million wireless customers are concentrated in areas including Milwaukee, Oklahoma City and Tulsa, Okla.

Gabelli’s firm thought it was close to persuading Chairman LeRoy Carlson Jr. to sell a few weeks ago when it took him on a road show to meet hedge funds, two sources with direct knowledge of the road show said.

The optimism was outlined in a March 16 Gabelli & Co. report.

“There is a 50 percent probability of [US Cellular] or a meaningful portion of its assets to be monetized over the medium term,” the report said.

Gabelli said in the report the net asset value of US Cellular was $6 billion, equal to $71 per share.

Despite the upbeat report and the fact that Carlson — a member of the US Cellular founding family — agreed to the road show, the executive, in the middle of the road show, dismissed the idea of selling the business, a source who met with Carlson said.

Carlson-family controlled Telephone & Data Systems, a separately listed company, owns 73 percent of US Cellular shares.

The family owns roughly a 10 percent stake in TDS, but controls it through super-majority voting rights and thus also controls US Cellular.

Verizon in late 2007 made a $100 a share offer for TDS, sources said, that was rebuffed.

TDS shares closed Friday at $26.31.

Gabelli Asset Management owns 4.2 million US Cellular shares, and 6.4 million TDS shares, which together are worth about $300 million, making it a top 10 Gabelli holding.

The firm has owned more than 4 million shares in US Cellular since 2005, when the stock was above $50 a share.

Gabelli declined comment, and US Cellular did not return calls.