It is difficult to pinpoint an exact date or even month when the Luftwaffe lost air superiority, because the Luftwaffe's defeat was a slow downhill spiral for about 18 months comprised of many smaller victories and defeats. There are 3 points along this timeline that could be considered the "loss" of Luftwaffe air superiority.
First, The allied bombing campaign against Nazi Germany was officially in full swing October 1943, and this is where the downhill slide begins. The Americans bombed during the day, and the British at night. The Luftwaffe had to begin contending with threats around the clock. Furthermore, the Luftwaffe was not yet concentrated at defending its home skies, but other fronts, primarily the Eastern Front.
Second, Mid 1944 is when the intensify was beginning to be felt in terms in 2 critically resources: fuel and experienced pilots. The Luftwaffe had plenty of aircraft and aircraft quality was debatably on par with Allied aircraft. However, if you don't have fuel and/or experienced pilots, having planes is worthless. Furthermore, mid-1944 was when allied escort fighters had arrived in sufficient numbers and with good tactics. This compounded the strain on Germany's war machine.
Third, in January of 1945, Operation Bodenplatte was the Luftwaffe lost any type of air superiority. It's fighter defenses were ill-spend on ground attack missions with ill-trained pilots, with much friendly fire. The losses in fuel and pilots could not be replaced. This was the final straw. From this point on, the Luftwaffe put up little resistance.