Since the death of JFK, America's power has waned in the world. There was Vietnam, the Arab Oil Embargo, the Iran hostage crisis, the Iran-Contra affair, at least two recessions, two other high-profile assassinations in the 1960s, the Gulf War, the Iraq War, the War on Terror, the list goes on. Kennedy was the last great ambassador for his country as its president. Since then, presidents just haven't measured up. Kennedy wasn't perfect, but he worked hard to earn what he did while he was president.
No, JFK's death did not mark the end of the American Republic, because the American Republic is still strong. JFK's death was a tragedy. The tragedy unified the people, and the country became even stronger after. Many of the programs that began in the 1930s, like the social security program, continued under LBJ as the war on poverty.