While the Allied powers did participate in a tank arms-race with Germany throughout the course of WWII, Germany didn't have much in the way of a clear technological advantage over their enemies as people think, but rather their advantage was more on the doctrinal level. German and Allied tanks were often very comparable on paper in terms of what people think makes a great tank (armor and the gun), and after the start of Operation Barbarossa, the Soviet Union had the simply better tank, with the Panzer III and early IV tanks unable to penetrate a T-34 or KV-1's armor, and both tanks very capable of destroying them, but what gave the Germans their early victories was their doctrine of Bewegungskrieg, War of Movements, better known as Mobile Warfare combined with close coordination with the infantry and air force. All these put together makes up the concept of Blitzkrieg. Sticklers will point out that Blitzkrieg wasn't an official military doctrine of Germany, but that doesn't absolve the term of its meaning and its effectiveness in practice.

To step back a bit, by 1939, the concept of tanks and armored warfare was only barely 23 years old, and all the major powers had different ideas of how to apply tanks on the battlefield. Britain and France, for example, saw tanks as working closely and in tandem with the infantry to support and move with them. This concept of the infantry tank led to the development of heavily armored but painfully slow vehicles that would in theory push a front line until it breaks (i.e. Char B1, Churchill, and Matilda tanks), allowing infantry to exploit the breach made by the tanks. Britain further expanded on this with the concept the cruiser tank (the Crusader, Covenanter, and Cromwell tanks), a fast, but lightly armored vehicle that could rush through a break made by the infantry tanks and further exploit their advances and wreck havoc behind the front lines, much in the same way as horse-mounted cavalry would in pre-armored warfare.

Germany pioneered a different doctrine when it came to tanks through. With General Heinz Guderian as the man receiving the most credit with Germany's armored doctrine, he envisioned dedicated Armored (Panzer) divisions divorced from infantry divisions that could move independently of infantry divisions. With emphasis on communication between multiple Panzer divisions and the Luftwaffe, tanks could rush through positions that have been softened by air bombings from the Luftwaffe at high speeds and coordinate with other panzer units to encircle and destroy enemy positions. This was achievable through widespread radio communication between tanks in order to coordinate attacks on a scale impossible to other communication means practiced by the British, French, and Soviets, who relied on signal flags to communicate for the most part. While only certain command tanks of the Western Allies had radios, Guderian stressed the need for a radio in every tank in order to effectively coordinate and maneuver effectively. This absolutely paid off dividends in practice, with German tanks outmaneuvering Allied positions rather than just outright muscling through them as infantry tanks would be designed to do. Panzers would coordinate and move so quickly that allied commanders couldn't effectively respond to the rapidly changing developments. The course of events would move so fast that by the time a commander received a situation report from a position and issue them orders in response, the position reporting would be overrun before his orders could even reach the position, taking advantage of mass confusion among Allied formations for even more effective results.

Germany's doctrine of combined arms warfare, with fast moving and well-coordinated tank movements supported from the air, was successfully replicated again and again in Poland, France, the Balkans, and during the opening stages of Operation Barbarossa.

So what happened to eventually stop and later counter Germany's doctrine? And was it Allied technology catching up? well yes, but not in the way you're thinking in terms of tank effectiveness, but tank communication. The Allies definitely learned their lesson from Germany's striking victories from 1939-41, and began incorporating many of the same tenants as German panzers. The Soviets reformed their Tank Corps to be more independent of the infantry and with improved communication to work much like a panzers, and counter-tactics to the blitzkrieg were put into action such as holding the shoulders of a breached line, which could be vulnerable to counter and in turn encircle the armored spearhead that was meant to encircle their position.

What made Germany's tactics suffer the most though, more than the Allies upgrading to the 76mm/17 pounder/85mm guns was Germany's shortfalls in resources and supplies, with shortages leading to Germany's panzer divisions being less and less offensively capable as the war dragged on.

Tank logistics are a nightmare, and require constant supplies in order to keep itself running effectively. Without even one major logistics need sufficiently provided, an offensive can prove to be quite impossible. Beyond Germany's obvious and well-talked about shortages of oil to sufficiently fuel thousands of gas-guzzling metal boxes, there's spare parts to think about if the tank breaks down, and that's a lot of parts for a lot of different breakdowns. Sand and dirt clogging the air intake of the engine? You're going to need replacement filters or, god forbid, a new engine entirely if the damage is too extensive. One of the axles breaks and destroys a good chunk of a Tiger's overlapping and interweaved roadwheels, that's going to need a lot of spare wheels. The final drive of a Panther breaks down only 150 km into its service life? oh boy you're going to need a brand new transmission. Germany simply could not make enough spare parts to cover mechanical failures, repairs, or sufficiently refuel their tanks, and as the war dragged on and factories capable of making these already scarce parts are bombed out of production, the situation gets desperate and broken tanks are just left to their fate. While Germany's capacity to conduct offensive operations became weaker and weaker, Soviet, American, and British capacity to produce, fuel, supply, and replace their forces only became more effective as the war went on, with the combined industrial capacity of the US and Soviet Union eclipsing Germany's ability to produce war material 50 times over.

While what you said is true about the Allies developing counters to German armor with new tanks like the Sherman Easy 8 and the IS-2, these played a minor role in the breakdown of Germany's tank tactics on the operational level, with attrition and inability to replace losses factoring more into Germany's inability to conduct offensives with their tanks.

Sources:

No Room for Miracles. German Industrial Output in World War II Reassessed by J. Adam Tooze

When Titans Clashed: How the Red Army Stopped Hitler by David Glantz

Tank Warfare on the Eastern Front, 1941–1942: Schwerpunkt by Robert Forczyk

Achtung Panzer! by Heinz Guderian