Why did Denmark win the Battle of Heligoland but lose the German-Danish War?

The Danish victory at the Battle of Heligoland on May 9, 1864, was a tactical naval success that failed to alter the strategic outcome of the German-Danish War for several reasons:

• Military Disparity: Throughout the conflict, Danish forces were consistently outnumbered and outgunned on land, particularly regarding artillery. Following the loss of the Danewirk and the defeat at Dybbøl, the Austro-Prussian army occupied Jutland, leaving Denmark in a position of military collapse.12
• Lack of International Support: Denmark’s diplomatic efforts to maintain its territorial integrity failed. Major European powers, including Russia and Great Britain, were either unsupportive or unwilling to intervene, leaving Denmark isolated against the combined strength of Prussia and Austria.2
• Limited Scope: While the naval blockade was effective, the victory at Heligoland was a relatively small engagement that could not compensate for the overwhelming losses sustained on the battlefield.12

Ultimately, these factors forced Denmark to sign the Treaty of Vienna, resulting in the surrender of Schleswig and Holstein.32