At what point could Britain no longer win a war against the United States?

Probably around 1800 (if we are talking reconquest of the US) or 1860 (if we are talking any sort of real concessions.) After that the Americans are strong enough to conquer Canada and as much as a Royal Navy blockade might have stung I don't think it could have won the war alone for Britain.
...If you define "winning a war" as a naval war for control of the Seas, I would say either side could win for most of the 19th century, though the conflict would more likely than not go in Britain's favor. Even in 1812, though, they failed to win a full victory at sea...

That rather depends on how you define a full victory. America's navy achieved early successes in the War of 1812, particularly in single-ship engagements due to the superior firepower of their frigates in the early stages of the conflict. However, the British quickly countered with larger frigates of their own and with squadrons. Even with their focus on Napoleon, the Royal Navy at the time could and did heavily outnumber and outgun American ships in American waters. By the end of the war, the Atlantic campaigns had become almost comically one-sided. The British blockade strangled American trade to the point that most of its warships wouldn't leave harbour and only about 5-10% of American merchantmen were willing to risk running it. Meanwhile, the UK's own trade and ability to ship supplies and troops were so unaffected that insurance rates didn't even rise. If the UK had been serious, really serious, about fighting and beating the US during that period of time, America wouldn't have had a chance.

On land, the US was unable to make headway into Canada in 1812 even though the UK deployed fewer troops to North America during the entire War of 1812 than they suffered casualties during the Peninsular War. The US may have had nothing to contend with except a (comparatively) tiny number of British soldiers, Canadian militia, and their Indigenous allies, but those were more than sufficient to force a draw in the War of 1812 when England had no interest in seriously prosecuting that war to the best of its abilities.

By 1812 it's probably not feasible for the UK to try to reconquer the US, but the UK can crush America's economy and blockade it without jeopardizing its commitments elsewhere, even when those commitments are as large as the Napoleonic wars. The US, on the other hand, is proved totally impotent in 1812 to harm British interests even in North America. It would take quite a few decades after that conflict before the US could guarantee a draw in any hypothetical conflict, let alone have a chance at actually winning.
The American Economy was hurt but far from crushed, in fact industrial production rose.

American Privateers captured 1,500 British Merchant ships. Insurance rates were high for the last 20 years of war, and wouldn't fall until peace was reestablished. The RN was unable to control the Privateers, because the blockade of America was harder then France due to the length of the coast, and the RN was far away from it's bases. The USN controlled the Great Lakes, and internal waterways making invasions from Canada impractical. The fall of Washington was a national disgrace, but was effectively a raid. The British were unable to take Baltimore, or threaten any other major American Cities. The British Army was far more casualty averse then the Americans.

The American problems were poor organization, and national divisions. The New England States refused to fight, and traded with the enemy. The organizational problems were being worked out, and American Forces were fighting more effectively in 1814, then in 1812. The defeat, and death of Tecumseh, and his Indian Federation meant there would be no Indian buffer zone between Canada, and America, so there wasn't any territorial goal for the British to fight for. If peace hadn't been concluded in December 1814, it would have been in April 1815. With the news of New Orleans, and the return of Napoleon from exile the British would want the war over now. Both sides had made their point. With the end of the Napoleonic War the Major causes of the war were made moot.
In answer to the original question.. we haven't reached that point yet. OK, that needs some clarification but as this seems to have evolved into a "The US can successfully invade the UK" debate I can only say that no they can't! Overwhelming Air Superiority, overwhelming Naval Superiority and overwhelming Land Superiority count for very little if you are unable to project that power to where it's needed. The North Atlantic may not look that big when you open up Google Earth but is still a serious distance when you are talking about transporting a million men to a hostile country. From a purely logistical standpoint the US is incapable of launching a successful invasion of the UK at the present time if such a scenario would ever arise.
I think people are focusing far too much on the landing troops and direct combat aspect of things. Modern warfare is not always about that. For all the aloofness that being an island has allowed Britain to be, it also presents a huge drawback that to some extent was seen during WWII, it makes it easy to cut off contact with the world. If the US wanted to it could use the USN and USAF to institute a blockade of Britain and starve them (of food, oil, etc) into submission. Boots on the ground just aren't necessary, or at least aren't until the industrial machine starts grinding to a halt. At the end of the day, that is what helps US power projection far more so than any amount of troops do. The US is capable of projecting enough power to halt the war machine of most countries in the modern age if it wants to, and from their its just a matter of cleaning up the scraps.
Glad to see that we have moved away from the Fantasy Invasion of the UK and are talking about a more plausible means of waging war. A blockade might well bring the UK to her knees, but which type?
A distant blockade is going to be terribly difficult to achieve bearing in mind the huge numbers of shipping heading towards Europe from the rest of the world. Would the USN have to blockade the straits of Gibraltar as well as the Suez Canal in an attempt to stop supplies being slipped in the through the back door (otherwise known as Europe)? If so the USN is going to be very busy if pursuing a stop and search policy. Or would it have to follow an unrestricted policy and sink any vessels that are steaming anywhere near the UK? Could the US afford to upset any potential allies in such a situation?
A close blockade is nowhere near as practical, although if it were achievable it would strangle supply from Europe. Without allies this is going to be a really tough challenge for the USN. To close blockade an enemy coast so far from its own, with the need to rotate the units and resupply them, whilst being so close to the UK, the US is almost certainly going to need the support of some regional allies. I have been looking at this thread with the US and the UK being sole participants in this conflict. If this is indeed the scenario then this is going to be difficult for the US. When Great Britain blockaded Germany during the First World War it did so being able to close the Channel and the exit of the North Sea into the Atlantic with the advantage of having established naval bases close to each. OK, and the RN also had convincing naval superiority.
I suppose, lastly, that wars can also be determined by a political will to either continue regardless to, or give ground in the respect of, the opinion of a country's own citizens. I'm no expert on US History, but it might perhaps be argued that the Vietnam War was lost on the streets of the US rather than in the rice fields of Southeast Asia.