One morning during the next five years, you’ll wake up to news that HBO has seen the light. The cable network will announce that it has decided to take your money — maybe $12, $15, or $20 a month — and from that moment on, you’ll be able to watch its shows without a cable subscription.

Execs at the network and the rest of the TV industry will hail the news as momentous. But don’t be surprised by it. I’m not going out on a limb in making this prediction, because what happens from here is slam-dunk obvious: HBO’s current business is doomed. Yes, the network is riding high now. But there are simply too many growing forces arrayed against its cable-dependent model for the business to continue as it is — too many high-quality shows from competing, non-premium cable channels, too many new technologies for watching TV, too many startups gunning for HBO’s customers. At some point, too, there will simply be too much money in the streaming business for HBO to ignore.

The only question now is, When? Or, more to the point: When HBO does come around to breaking free of cable, how late will it be? Clearly the ideal time to make this move is right this minute. Or, actually, it was two weeks ago, just before the “Game of Thrones” finale. In addition to the immense popularity of that nerd-bait show, HBO currently benefits from a struggling Netflix and Hulu, and a TV industry that hasn’t yet been completely remade by Apple, Amazon and Microsoft. If it had booked a few million non-cable subscribers now, and then slowly expanded on that effort over the next few years, the company could well have set itself up as a leading player in the new, many-device, multi-payment model TV world.

But instead HBO is dithering, playing chicken with an unyielding future. How disastrous will this course prove? When HBO finally, inevitably decides to offer non-cable subscription plans, will it be just fashionably late, at a point where it can salvage its future? Or will it be so perilously tardy that it can’t catch up? At the moment, when it comes to streaming, the men who lead HBO seem bent on sticking with this second strategy — better never than late, as they see it.

The idea that HBO’s future is in any way dire might surprise you. HBO today is an exceptional media business, the crown jewel of parent company Time Warner’s content offerings. As Dan Frommer points out, Time Warner’s network segment — which includes HBO and all the Turner Broadcasting channels — generated $3.6 billion in revenues in the first quarter, half of Time Warner’s entire take. More importantly, almost 90 percent of Time Warner’s profits came from its TV networks. Time Warner doesn’t break HBO’s financials apart from Turner, but estimates by the research firm SNL Kagan put HBO’s annual revenues at close $4 billion, and its profits at more than $1 billion. After a fallow period of not too many very popular shows, HBO’s programming has once again become the talk of the town — the second-season premiere of “Game of Thrones” in April eclipsed “Mad Men” as the most-watched scripted drama on TV. As a result, the company expects revenue growth to accelerate in 2012.

But HBO has two looming problems it can’t seem to solve. Its subscriber growth in the United States is flat, and it has remained flat for several years, even while competing premium channels surged. About 28 million people in the U.S. now subscribe to HBO, but — as The Economist explained in an in-depth profile last year — there is tremendous “churn” in its base, with about 10 million people dropping the service every year, and a more-or-less equal number signing up.

It would be bad enough if just HBO’s growth was flat. But HBO’s subscriptions are a function of the larger market for subscription-based TV (i.e., cable, satellite, or TV-by-telephone providers like AT&T) — and that market is slowly declining, with about 1.5 million households cutting the cord in 2011. In other words, the total addressable market for HBO is shrinking.

And, finally, HBO is also threatened by the troubled economy. The Economist pointed to data from the research firm GfK MRI that shows that many of HBO’s customers are struggling to pay their bills. About 35 percent of the network’s subscribers are in the poorest two-fifths of American households. If the economy continues to struggle, how long will these people stick with a luxury TV network?

These numbers would seem to paint an obvious path for the network: HBO’s current subscriber stream is drying up, and it needs to find a new clutch of customers. So what’s it doing? It’s choosing to ignore the problem. Instead, HBO is focusing relentlessly on international expansion — about a third of its revenues now come from outside the country — and, domestically, its main goal is to reduce churn. That’s the purpose of HBO Go, its streaming service for current subscribers. The theory is that if customers can get HBO in more places, maybe they won’t be so quick to drop it every year.

For a network that completely remade the TV business—for a network whose most popular show brims with dragons and zombies and other out-of-this-world creatures—the idea that the best HBO can do is hang on to current customers sure seems to lack imagination, doesn’t it?

HBO’s strategy seems especially bizarre when you consider how obviously attractive its non-cable streaming plan could become. Even though Netflix has made several boneheaded moves over the last couple years, and even though it barely offers any exclusive content, it now has 23.4 million streaming subscribers in the U.S. The company projects that it will add about 5 million more through 2012, meaning that by the end of the year, it will likely have eclipsed HBO’s domestic subscriber base. And Netflix will continue to grow after that, while HBO will remain flat as long as it stays nestled in cable’s bosom.

Netflix’s strategy proves that there’s a vast audience willing to pay a few dollars a month for premium content outside of their cable bill — a much bigger audience, actually, than the number of people willing to pay for premium TV through cable. Considering HBO’s vast library of films and shows, a streaming offering at prices comparable to Netflix’s would be an instant winner. And when HBO does finally offer a streaming plan, you’ll probably get it or Netflix’s, but probably not both. Thus, to the extent that Netflix is getting a head start in this market, HBO’s window of opportunity closes by each passing month.

Wait a second, though. Can HBO afford to go beyond cable — after all, doesn’t it rake in huge monthly premiums through cable customers, an amount that it could never get hope to match from people who don’t pay through their cable bill? Well, not really. Dan Frommer notes that he pays $17 a month for HBO, which is more than the average of $12 a month that Twitter users said they’d be willing to pay as part of a campaign inspired by TakeMyMoneyHBO.com.

But when you pay for HBO through your cable bill, HBO does not get all your money. Instead, it gets only half, and your cable provider gets the other half. After fees to cable companies (including its own parent company, one of the nation’s largest cable firms), HBO makes about $7.27 per subscriber every month, says SNL Kagan.

Guess what? In the first quarter of 2012, Netflix made $507 million in revenue from its 23 million American subscribers — which comes out to $7.22 per month.

In other words, HBO and Netflix are in exactly the same business. The two companies make the same amount of money per customer — except that by going through cable companies, HBO needs to charge people twice as much as Netflix does, and it also must grapple with an arbitrarily capped total market.

How does that make any sense at all? It doesn’t. Not too long from now, this truth will dawn on HBO. But will it do so before winter arrives?