Strictly speaking, the German Confederation no longer existed when Bismarck kicked the Austrians (and de facto Liechtenstein) out of it in 1866, following the Austro-Prussian War. Luxembourg was also out, and many of the states such as Hanover were annexed by Prussia, which subsequently established the 'North German Confederation', essentially Prussia & Friends.

Following the end of WWI, Liechtenstein drew closer to Switzerland, so I'd imagine that part of the reason that the tiny kingdom survived WWII was because the Nazis did not want a confrontation with the Swiss. The Swiss did supply some weapons and materiel to the Germans, and handed over the contents of Swiss bank accounts belonging to German Jews. Swiss francs were also some of the only foreign currency the Germans had access to, as almost no one would accept German Marks. Pissing off the Swiss, then, was not a wise option for the Germans, although they did have plans for invasion (operation Tannenbaum).

As to why Austria still exists, Austria was allowed to unify in 1955, and from that point on continued to develop it's own identity as a state. Germany was split in two at this time, and only unified in 1989, by which point independent, post-war Austria had existed as a distinct entity for almost 4 decades. The contentious status of Austria as 'Hitler's first victim' also had a role to play in the immediate aftermath of the war.