The answer to this is really three factors. First is that the Luftwaffe suffered more losses than it could sustain. This was most evidenced by the Battle of Britain. In that conflict, a Luftwaffe with a strength of about 5000 combat aircraft lost as many as 1800 combat planes over a four month period. That is unsustainable by any metric. They also lost significant numbers of planes on the Eastern Front in the four years leading up to Normandy. This page: http://chris-intel-corner.blogspot.ca/2012/04/eastern-front-aircraft-strength-and.html estimates that the Luftwaffe lost approximately 11000 aircraft on the Eastern Front alone. From a starting strength of about 3000 we can start to see how this could be a problem. You are talking about replacing almost your entire combat force every year! On the other hand, the Soviet Airforce lost way more aircraft and aircrew. The answer is that they simply were producing more aircraft and training more aircrews. German fighter production was always substantially lower than either the Soviets or Western Allies. So, even while the Soviets suffered comparable rates of losses in the early years of the war vis a vis their total strength (German pilots continued to demonstrate significantly higher victory ratios than their Soviet counterparts), the Soviets not only managed to replace those as the Germans had, but expand. And here is the second part of the answer.

Let's compare relative strengths on the Eastern front. In 1941, the Luftwaffe had approximately 2000 combat aircraft to the Soviet Union's 4000. Huge numbers of aircraft on the Soviet side were lost in the first few weeks on the war, many on the ground. Even so, by 1942, that number had gone up to about 6000, 12000 by 1943, and by D-Day 15000. Meanwhile, throughout this period, the total strength of the Luftwaffe remained about the same as it was in 1939. With these numbers in mind, you can start to see how the Luftwaffe would struggle. Ultimately, most historians would argue that the German armaments industry in general was inferior for much of the war in terms of efficiency, and aircraft production was one of the worst culprits for this. Indeed, it wasn't until Albert Speer took over and reorganized production that it began to increase to what it was needed to meet the demands of war, but this was a little too late. Indeed, more than half of all German aircraft built in the war came in 1944/1945, with '44 representing almost half by itself. However, by this time, it was of course a bit too late.

Finally, the third part of this answer is that, simply put, when you combine the rate of losses and the growth of the Soviet Airforce, you also have to factor in the role of the British and US. One of the biggest challenges that faced the Luftwaffe in June 1944 was that despite being basically the same size as they were in 1939, they now had many more responsibilities. For example, by 1944, as high as 50% of all German fighter assets were being diverted to anti-bomber duties, taking these aircraft out of front-line duty supporting air superiorty missions on the front. US and UK bomber missions had a debatable impact on German industrial production, but there is no question that they significantly weakened front-line combat ability by diverting combat aircraft away. Then you also have to factor in the actual influx of Allied fighters into the west. We are talking about an additional 4000+ fighter aircraft.

Let's put it all together. So, first we have singificant Luftwaffe losses. Second, we have the Luftwaffe's inability to keep up with the growth of the Allied airforces. Lastly, we have simply too many responsibilities to devote those planes to. By June 1944, Luftwaffe combat strength on the Eastern Front had fallen from the 1941 high of 2000 to to less than 1,500. They had gone from nearly 1,000 fighters to less than 500. To put in better perspective, they had gone from having 2.5 Soviet Fighters for every Luftwaffe fighter, to facing about 16-17 Soviet Fighters. In the west, a couple hundred Luftwaffe fighter aircraft were responsible for defending against those 4000+ fighter aircraft, a ration of nearly 20:1 in favour of the allies. Hitler's answer to these were aircraft like the Me-262, but even these wonderful aircraft could not stem those kinds of numbers.

There are a few ancillary reasons for this as well. The dwindling fuel supplies of the Luftwaffe made even the small number of aircraft they had even less effective by 1944. In addition, by 1944/45 their aircraft were beginning to show their age. The Stuka, one of the iconic weapons of the early war, was particularly showing its age; by then it was an almost a decade old design. The Bf-109 was also nearly a decade old by this time. Meanwhile, allied front-line designs like the P-51 or the Yak-9 were significantly newer. Even if one argues that these newer designs simply brought American and Soviet aircraft to par with German fighters, that is not good news for the Luftwaffe. The Red Army, British, and French air forces in the early war period were all primarily composed of older aircraft in large numbers. So, if we go back to the ratios above, while the Luftwaffe might have faced 2.5 fighters for every one of theirs in 1941, many if not most of them were inferior planes to their own. By 1944, many if not most were at least on par, and it wouldn't be difficult to argue that Soviet aircraft were superior by the end of the war in many ways (particularly in the ground attack role). Ultimately though, a 20-1 numerical superiority is basically insurmountable in my mind, so it really does come back to that. I think we can summarize all this with the short answer of: Germany bit off way more than it could chew in the war, and didn't really commit to total war industry until 1943. The same reasons for poor aircraft production were mirrored in almost all aspects of German armaments production in the early-war period.