We will overcome any problem in our path. If microstates are able to survive, they most certainly can, and most definitively will.
In 1962, France wanted tax concessions from Monaco, even going to the extreme of wanting the tiny city-state to join it. At that moment, Charles de Gaulle, an important politician in recent French history, ruled the Republic. Whilst it is not covered much today and the only popular-ish movie that takes place on the event concentrates in the American Princess Consort of the time (which makes Monaco's royal bloodline FREE AND 'MURICAN
), Monaco managed to survive. If Monaco, a tiny nation smaller than the municipality I live, managed to reach an agreement on existing, then it has the will and strength to do so, despite being 2 km2 big and 20% of its land has been reclaimed from the sea.
This is not the only incident this country has faced: the 1861 Franco-Monegasque Treaty, the 1790s annexation by the French Republic, and the fact that it currently exists means that microstates can solve these and many other problems. This is impressive, as these nations are microscopic on our maps. They, like many other nations, can be flexible and cunning to live as nations, not just another part of their surrounding neighbour.
Singapore's case is unique. Being founded as a lucrative outpost by the British Empire, migrants of all walks of life and of the surrounding countries flocked to it. Its principles of free trade and its geographical position made it wealthy. After the Japanese occupation (if I am not mistaken), Singaporeans wanted to rule themselves. Singapore became part of Malaya, which made the two into Malaysia, in order to be free of the British Empire. Malaysia broke up, however, as race riots in and disagreements with Singapore forced Malaysia to expel it from the union. Despite having a sour neighbour to the north, Singapore forged a national identity, whilst being a tiny island. It became the nation it is today.
The Vatican is peculiar as well. It is the remnants of the Papal States, which suffered extinction after the Italian unification movements and wars forced it to cease to exist. However, the Catholic Church authority withdrew to the Vatican. The Pope didn't recognize Italy, as well complaining of being a prisoner in the Vatican, and Mussolini, in order to score points with Catholics and deal with the issue, signed the Lateran Treaty, and Vatican was forged into its current shape.
This is how I remember it, so some facts might be wrong from Monaco, Singapore, and Vatican.
Microstates have endured the test of time. We might see most of them as pathetically weak and fragile things that shouldn't exist, but they do (heck, Singapore has a highly advanced military to boot). They are odd, but they are steel-clad when facing adversities which could end their stay on this Earth.