The Arlington County Board voted last night to give Arlington Telecommunications Corp., the firm that operates the county's cable television franchise, a six-year franchise extension, from 1985 to 1991, despite complaints against cable service voiced at a series of public hearings. d

ARTEC, as the company is commonly called, had appealed to the board for an early renewal, claiming that it was threatened with bankruptcy and that an extension would permit it to obtain financing. The company became operational only a year ago and now serves an estimated 20,000 county households.

The board reached its decision after about 18 hours of public hearings in the last month -- one of the longest debates on any single issue in the county in recent years.

In the course of that debate, ARTEC was criticized by a broad segment of the community and admitted its failure to meet some contractural agreements with the county, such as providing an equipped production studio and public access programming opportunities.

But several board members expressed a belief that it was too early to once again go through an open bidding procedure for the franchise, as many of ARTEC's critics proposed, and chose instead to give ARTEC a second chance. The board originally awarded the franchise to ARTEC in 1973 and it went into effect in 1975.

The extended franchise is intended to give ARTEC officials a chance to seek long-term financing on nearly $6 million in short-term debts. Last year the company paid out more than 20 percent of its revenues on interest.

Although the cab le tgelevision industry is considered extremely lucrative in the long run, industry analysts say the high cost of stringing cable to subscribers means that most cable companies must wait up to 10 years from the start of transmission before receiving a return on their investment. ARTEC's supporters said the company ran into trouble because unforeseen problems, including the death of an early company officer, delayed the system's start for three years.

Complaints against ARTEC at the hearings included objections to installation delays, poor reception and failure of the company to live up to its agreement.

But Board Chairman Stephen H. Detwiler, who is a banker, defended the board's action, saying, "I don't look at this as a refranchising in any way, but as a recognition that from 1973 to 1979 there were a lot of problems with the [cable] industry. To say that we have had a system for 10 years is not factual."

The only one of the five board members to vote against the extension was Dorothy Grotos, who said, "the board has been very cooperative with ARTEC. Are we going to let them off the hook, let them come in the back door?"

The board is expected to consider specifics of the new franchise agreement in September.