This depends entirely on your point of view: it's either from the very beginning in 1939, or in 1941 with the failure of the capture of Moscow during operation typhoon.
Wages of destruction by Adam Tooze offers some pretty good reason for this. The economic balance of power was always very much against Germany once war broke out. Even in 1940, the UK and France was outproducing Germany in terms of war materials (i.e in terms of warplanes). Also the Nazis were chronically short on raw material and lack the means of importing them from oversea sources (To give you some idea of how bad this was, Germany was almost out of bombs following the invasion of Poland) whereas the Allies had the resources of the entire colonial empire to draw on. Meaning that any real war of attrition or long term war was going to result in German defeat.
So what the Germans needed to do is not to wait for a war of production to occur, but to push forward with the conquest of new territories as fast as possible in order to secure new resources and to knock out opponents before they can translate their economic potential into military power.
To this end, daring Blitzkrieg attacks were the optimal strategy, as shown in the invasion of Poland, France and the first 6 month of the invasion of Soviet Union. The Germans also enjoyed very good luck (i.e much of the French airforce was grounded for maintenance during the first phase of the invasion of France), and very very bad planning on the part of the Allies (i.e during the invasion of France the French rushed armored divisions into Belgium, walking right into a German encirclement) that made it very successful during the first stage of the war.
However, the problem with this strategy was that it depended very much on momentum, the moment when a conquest is stalled or failed, the house of cards starts to collapse because the war turns from a rapid war of maneuver and encirclement into a slow war of grinding attrition and production. I cannot stress how important this is because Germany's opponents to both the east and the west was growing stronger faster than it was. There was therefore, a limited window of opportunity to launch a successful invasion. Delaying the invasion of the Soviet Union by a year for instance, would have meant the Red Army recovers more from Stalin's purges and fix the problems it was shown to have during the Winter war with Finland which drastically decreases German chance of success.
As an aside, the invasion of the British isles was never a serious option for the Germans with any possibility of success.
And a stalled conquest is exactly what happened in 1941, the German failure to capture Moscow when it invaded the Soviet Union. German forces stalled in front of Moscow in December 1941 and subsequent Soviet counter attacks drove it from the gates of the Soviet capital. By failing to do so, it failed to knock out the Soviet out of the war and was therefore forced into a war of production. The declaration of war on the US in 1941 after Pearl harbor did not help in that regard.
Thereafter, despite retaining control of most of Europe, the Nazis was unable to mobilize the full extent of industry because Europe lacked natural resources to do so. The chronic shortage of oil, Bauxite among other materials mean that many factories in occupied territory lie idle. There are a lot of myth regarding the fact that Germany did not go on war economy until it was too late while in reality the truth was that Germany was -unable- to mobilize the full economic potential of its occupied territories.
By Paul Kennedy's calculation, the US alone possessed over 50% of overall war-making powers (industry, manpower etc) in the world in 1941, combined with Soviet and British production, it was only a matter of time until Germany was grinded down by superior economic power. For a while, Germany retained an advantage in being the most experienced of the combatants with the best quality army, but that started to disappear as the Red Army started to gain more experience and Germany's best divisions was destroyed on the Eastern front. It was able to achieve important tactical success on all fronts (i.e 3rd Kharkov, Kasserine Pass), but those were never enough to change the balance of power int he war. The rest is, as we say, history, as the allies defeated Germany and occupied it.
Had the Germans taken Moscow in 1941, it would have captured an important center of transportation, it would have dislocated the Soviet planning bureaucracy which made its economy work, and most importantly it might have caused a political collapse within the Communist party of the Soviet Union, which might have destroyed the Soviet war effort. Once it occupied enough of the Soviet Union, it might have being able to acquire enough natural resources to mobilize the industry of Europe and transfer enough divisions to the west to prevent an Anglo-American landing. But even that is a pretty long shot because chances are the Soviet Union will not collapse following the loss of Moscow.
The Nazi regime was pretty inefficient and there was a lot of stuff they could have done better (i.e rationalize the production process instead of having an ad-hoc allocation of raw material among its industries), but none of it as enough to fundamentally alter the economic balance of power.
tl;dr Germany was a the equivalent of a RTS player whose entire build was to go for a one base all in tank rush while everyone else had economic builds, as soon as the tank rush starts to fail loss is inevitable.
That one is tough to pin point exactly, but things generally started going down hill in late 1941 when Operation Barborossa (more specifically Operation Typhoon) stalled at the gates of Moscow. The cold actually inflicted more casualties on the Germans than the Russians did. So the lack of preparation for the winter, coupled with a devastating Soviet counter attack with fresh siberian divisions devastated the Wehrmact and pushed them back but did not break them.
While taking Moscow probably wouldnt have ended the war, the eastern front is where the war would be won or lost by the Germans and i believe Hitler's constant meddling, disregarding of his generals and obsession with being on the offensive is what ultimately cost Germany the war. He pushed for offensives, despite urges from his generals to fall further back to a more easily defendable position at the end of 1941, refusing to give up territory already won led to tremendous and unnecessary casualties. The German army while tactically superior was no match for Russia in a war of atrition and needed to be smarter with their limited manpower.
Hitler pushed for an offensive in June 1942 codenamed "Case Blue" to attack south into the Cacuses, again despite insistence from his Generals that an offensive that year would ultimately be disastorous as they needed time to rearm. The Germans had just started to pump out the tiger/panther tanks and they were not entirely battle ready as would later be proven. As well, the first jet fighter was close to completion but Hitler wanted it redesigned for the light bomber roll thus delaying it by many months.
Anyways, to answer your question, i think the nail in the coffin for the German Army was at the earliest December 1941 with the failure of Operation Typhoon and the declaration of war against the USA, and December 1942 at the latest which saw Case Blue fail with the destruction of the German 6th army at Stalingrad.
The defeat at Stalingrad physically broke the back of the Wehrmact militarily and the declaration of war against the USA in late 1941 made victory nigh impossible as they could never hope to compete with the both the manpower of the USSR and the economic strength and supply of the United States.
I'd say at the time the UK decided to stand and fight With all continental allies gone the Germans had a chance to strangle UK supplies and even perhaps press in the Suez Canal as they intended once they landed in North Africa, but by the time the British decided to resist the US was already backing them and unofficially US destroyers escorted the vessels heading to the UK, provide anti-submarine patrols from Iceland and openly supplied the UK with goods and armament. With or without the invasion of Russia Germany was a crippled economy by the start of the war and could not maintain the state of war indefinitely, may had taken longer, may had led to negotiations but to me at that point Germany would never emerge as victor, may be a draw and a negotiated peace but not as a winner. But this is "what if" history, it happened what it happened.
As a side note, this is quickly becoming one of my favorite sub-reddits...