When Venezuelans took to the streets this week to demand a return to democracy, they chose a date with deep historic significance: Jan. 23, the day a dictatorship collapsed in the face of surging protests more than 60 years ago.

But demonstrations alone didn’t bring down Venezuela’s strongman back then. Only when the military stepped in, with tanks alongside protesters, did the dictatorship fall.

It’s a playbook that Juan Guaidó, the 35-year-old opposition leader who declared himself Venezuela’s rightful president to cheering crowds on Wednesday, hoped would be just as relevant today as it was in 1958.

While Mr. Guaidó earned the official recognition of the United States and more than 20 other countries, he remains a leader without a state. Venezuela’s military brass publicly swore allegiance to the nation’s president, Nicolás Maduro, frustrating the opposition’s plan to entice the armed forces into breaking ranks and turning the tide in the country’s long slide into authoritarianism.