Magid Advisors, which has commissioned its cord-cutting survey since 2011, reported a steady rise in the total number of subscribers who say they are "extremely likely" to cancel their service in the next year, from just under 2 percent in 2011 to nearly 6 percent in 2016.

The fall TV season is now in full swing, and with the return of football, tens of millions of people are tuning in to watch live and scripted programming on cable and broadcast channels. But according to a new survey, an increasing number of subscribers intend to get rid of their pay TV service in the next 12 months, and that number has been growing for years.

While Magid's survey measures intent to cut the cord, versus the actual number of people who have already cancelled their service, that intent appears to be translating into action.

In a recent report, BTIG analyst Rich Greenfield noted that "just a few years ago, the industry was adding video subs at a 1-2 percent rate." Now, he says, "the industry is losing 2 percent through cutting/shaving, not to mention the growing pressure from cord-nevers."

Among millennials, many of whom are so-called "cord-nevers," the picture is even bleaker for cable companies, with 9 percent of millennial respondents in Magid's survey saying they were "very likely" to cancel their service in the next 12 months.

Magid Advisors president Mike Vorhaus said the trend among younger audiences signals more subscriber losses in the future.

"When you think about the fact that there's an even higher number in the younger generation that's never had cable outside of their parents' home, not only do I think this is going to continue, but I think it's going to continue to rise in absolute numbers," Vorhaus told CNBC this week. Greenfield echoed a similar sentiment, writing, "we see no reason why subscriber trends will not continue to worsen."

As for the reasons behind the cord-cutting trend, Magid found that cost was not the driving factor, with less than a third of respondents citing cost as a reason for wanting to cancel their service. Instead, the majority of respondents said they were satisfied with the proliferation of over-the-top streaming options like Netflix and Hulu.

Vorhaus said that "skinny bundles" – or smaller cable packages that offer fewer channels – could be one way that cable companies can hold on to subscribers and combat the likes of Netflix and Hulu.

"We saw 52 percent of the respondents that pay for TV saying they want to do a skinny bundle," Vorhaus told CNBC. "I think this is part of the solution; it's going to keep some people that would have left otherwise."

Another way that cable companies could combat the lost revenue from fewer cable subscribers is by selling more broadband subscriptions. In a report from August, SNL Kagan projected an increase of 8 million broadband subscribers over the next 10 years.

Disclosure: Comcast, which owns CNBC parent NBCUniversal, is a co-owner of Hulu. NBC broadcasts Thursday Night Football.