There were strong scandinavist leanings after the danish lost Norway to Sweden and after Sweden lost Finland to Russia in the early 19th century. While certainly popular, the movement had little solid support from the upper echelons of Scancinavian society, and there was no obvious leader in the same way Prussia were for a german union. Still, there were some cautious cooperation between Sweden (with Norway in tow) and Denmark, especially among liberals.

This ended quite abruptly after the second Schleswig War of 1864, where the danish called on Sweden for assistance on Scandinavist grounds and the swedes refused, partly recognizing a lost cause, partly being on the german side. Though the movement has some support even today and contributed to the decision to use the same currency, though the nordic kronor has since diverged in value.

If we ask why in general we enter the realm of speculation which, as I've understood it, is frowned upon on this forum. Certainly though, the matter of relative power was a problem, both between Sweden-Norway and Denmark as well as the relative weakness of scandinavian states in international context. That there were no common language, no clear political center and no strong support from the political establishment were all contributing factors as well.

In fact, there were two Scandinavian unions in that period, in succession to each other. The first was Denmark-Norway, which lasted until 1814, and the second was Norway-Sweden from 1814 to 1905. These were not quite the same as the other two unifications, as these were personal unions of the Kingdoms and not a "nationalist" unification per say, so as far as I am aware the peoples were not integrated nor was one language promoted to become "Scandinavian." However someone with more expertise may shed some more light on this than I can.

In addition, there was also the Kalmar Union, which unified all the Scandinavian nations from 1397-1523, although I don't really know much about it.