It was. In point of fact, it had already been banned in a number of German states a year prior due to the increasing levels of street violence, as well as the assassination attempts - some successful - of government officials by far-right groups, the most prominent being Foreign Minister Walther Rathenau in mid-1922. Bavaria was one of the few where the Nazis didn't ban them at that point, as it was generally more sympathetic with right-wing movements.

Following the Putsch though, the Nazis were completely banned in Germany. During this period, the party kind of continued to exist illegally in a more clandestine manner, but with Hitler jailed, it was something of a headless chicken, riven by internal leadership squabbles and feeling quite directionless as Hitler rarely intervened from his comfy jail cell. In part the issue was solved due to the fact that there was little concern for enforcement, allowing new organizations which were Nazi in all but name to spring up, the principle one was the Greater German National Community, but the leadership squabbles continued, alienating many rank and file members, who left for other far-right groups.

As for why the Nazi Party was re-legalized, put plainly, Hitler had the right friends. With still four years left to serve, he was nevertheless released on parole despite opposition by the state in late 1924, although for those four years he had to be careful to obey the parole requirements. One aspect of this of course was that his party was illegal, and that wouldn't do. Meeting with Bavarian leader Heinrich Held were productive, and more importantly, that with Franz Gürtner, the Minister of Justice in Bavaria, who was a right-wing nationalist, and although not a Nazi, sympathetic. Hitler was able to easily convince them to lift the party ban in February of 1925, allowing Hitler to reform the party publicly (In Bavaria. It effectively banned in much of Germany until 1927, Hitler unable to speak publically, and in Prussia, a Social Democrat bastion, until 1928. Ironically, these bans were lifted because Hitler was seen as losing his pull so the bans were unnecessary). Promising to cooperate with the state, and be firm in his continued anti-Communism, it was a fairly easy sell by Hitler, and Gürtner would become Minister of Justice in 1933.

Importantly, this demise and resurrection allowed Hitler to reform the party explicitly on his terms. Although previously the leader, he had worked to gain that position within the existing party. For the reformed party, it was in no uncertain terms Hitler's Party, under his unquestioned guidance and leadership.

Sources:

Evans, Richard J. The Coming of the Third Reich

Kershaw, Ian. Hitler 1889-1936: Hubris