There were two interrelated reasons. One, the Luftwaffe did try to maintain a daylight aerial offensive against targets in London in September 1940. The attacks were a mixture of daylight and nighttime bombing raids. The largest daylight attack was on 15 September saw a major RAF response and significant German losses. The scale of the British response underscored that not only had the bombing offensives of the last few months failed to break the back of the RAF defenses, but that German fighter aircraft lacked the range to adequately protect the bombers in daylight over London. The Bf-109 only had a few minutes of flight time over London while the Bf-110 could reach the capital, it was limited in its efficacy. Although the Bf-110 was not the unmitigated failure postwar memory relegates it, its virtues- high speed and heavy armament- depended on surprise and slashing attacks. Escort missions denuded surprise and made it harder for the Zerstörer pilots to make the most of the 110's virtues. Daylight bombing missions over London meant Fighter Command could mass a response and the bombers would find their escort ineffective or evaporated too quickly.

The other reasons was that the attrition of both the Battle of Britain and the earlier Battle of France were incredibly hard on the Luftwaffe. The losses in the French campaign were quite high even with victory and the air battles over southern England only added to them. German training of replacements and manufacturing of new planes lagged behind these losses, which by some estimates accounted for a little over half of its May 1940 establishment numbers. The Luftwaffe probably could not have conducted a sustained, round-the-clock offensive even had the RAF response over London been much more anemic. The Kampfgeschwader could only barely meet its ever-increasing duties in September 1940. The night bombing of the Blitz not only resolved the thorny issue of fighter escort, but also provided a degree of respite for a severely taxed bomber force whose men and machines were wearing out. But even here, the Blitz was counterproductive over the long-term in that accident rates naturally climbed up, further weakening the bomber force so it actually conducted operations in 1941 as a numerically weaker force than it was in April 1940.

Just a minor point, as /u/kieslowskifan/ has covered the Luftwaffe in 1940 so well, but the Allies only really bombed around the clock from 1944. RAF's Bomber Command faced even greater challenges than the Luftwaffe in 1939-40: fewer aircraft with greater distances to cover to reach their targets and no possibility of fighter escort. Pre-war theory was that a close formation of bombers would be able to defend themselves using their gun turrets, but unsustainable losses in daylight raids over Norway and Northern Germany showed this not to be the case, for the rest of the war the vast majority of Bomber Command missions were flown at night.

When the United States committed to the Combined Bomber Offensive at the Casablanca Conference in January 1943 they also planned to mount unescorted daylight raids, US heavy bombers carrying more and heavier defensive guns than their British equivalents. Some on the British side, most notably Churchill, were sceptical; General Eaker of the USAAF presented a one page synopsis of The Case for Day Bombing to him and when it came to the sentence about round-the-clock bombing Churchill 'rolled the words off his tongue as if they were tasty morsels'. Once again, however, unescorted bombing proved unsustainable, missions such as Schweinfurt–Regensburg in August 1943 suffering heavy losses. Only when long range escort fighters able to accompany the bombers all the way to their targets started to be available in quantity from early 1944 were the Luftwaffe finally defeated and regular large scale attacks mounted both day and night.