I would say an island completely encircled by a naval force is toast in the modern era regardless of size unfortunately, but less so the farther back into history you go as technology and international trade become less and less important and we move back to a local agricultural society. (This is coming from someone with knowledge of European history specifically I should say.)

So if we go way back to say, ancient times, the Roman navy being able to control the English Channel in no way meant the ancient Britons were conquered. Similarly, medieval and early modern English naval power didn’t conquer Ireland for them (although Irish lords kept up their own galley navies and overseas contacts with Scotland and Man so that’s a complex issue). But the general point is that in a basically self-sufficient, highly localized agricultural society, being cut off from the sea is not the biggest deal. If those islands were going to be conquered, attacking armies were going to have to go in on foot.

What’s more, back at this point naval tech and logistics weren’t really up to maintaining massive, permanent blockades in the first place, at least in Northern Europe. Mediterranean galley fleets were rather more capable on this front. Indeed, sometimes you don’t need a navy or much of a navy the farther back in history you go simply because the logistical challenge of an ocean crossing in significant enough force to actually carry out a conquest was so high.

Generally though, when islands fight off attacks successfully it’s because they have navies strong enough to 1.) beat the invader’s fleet 2.) disrupt an invasion crossing 3.) maintain foreign trade to keep the island supplied. Venice was difficult to conquer because it was an island but also because of its navy—and as long as that navy was powerful it generally spared Venice from having to deal with sieges in the first place. Britain fought off or just deterred a variety of invasions from France from 1300 all the way to the Napoleonic Wars through naval power. I’d say not having a navy to resist is a pretty bad thing. Although obviously the strength of forces at home, coastal fortifications, ease of landing, location of ports, etc are all relevant too in this era.

But frankly, as far as I can see through most of history whoever has naval control of the sea tends to have control of islands even pretty far back. Look at how the Vikings were able to conquer so many islands—even when their mainland conquests got pushed out of or repelled eventually, they held onto islands far longer. Look at the medieval history of Sicily, which was constantly dragged under the control of whoever was the Mediterranean naval power and only has its moment of greatness under the Normans when it builds its own powerful navy. Look at the history of Corsica, which was also tossed between every naval power. Same goes even more so for yeah, basically every other Mediterranean island. There are some exceptions like Malta, which had some extraordinary fortifications—but Malta also spent a lot of its history aligned with greater powers—first Catholic powers through the Knights of Malta, then later the British Empire. Look at how dependent European Caribbean colonies in the early modern period were on naval protection, although again strong forts definitely could hold an island against a fleet in some cases. To your point look at how once the US had naval superiority in WW2 Japanese islands were doomed regardless of fantastic defense or fortifications. I would say the collapse in viability of coastal fortifications during WW2 particularly tilted the balance in favor of naval supremacy and against the defense of islands. Even in their heyday though, island forts generally only delay attack—to achieve victory, some outside relieving force will have to ride to the rescue sooner or later—unless the invaders can be relied on to die of disease (a handy factor in Caribbean island defense).

What’s more, the closer to modernity you get, the greater the importance of cutting off trade and connection to allies and empires grows because economies and militaries become increasingly globalized and complex. I’d say unless the island has oil reserves, agriculture and basically an entire industrial economy with mines of every substance, then getting trade cut off by an enemy navy is game over medium term. Think of Britain in WW2–desperately reliant on outside assistance—that’s what the uboat offensive was for. Think not just of pacific front island hopping but the American endgame for the Japanese home islands. In a modern context, an island surrounded by a superior navy can’t get some combination of new parts, oil, food, etc, not to mention a whole variety of civilian goods. That’s a game over.

I would say being on an island certainly helps a small nation’s independence plenty by raising the cost of an invasion from a simple march to the technical feat of a naval invasion easily disrupted by weather, navies, air forces and with a strong potential to be stalled out or overwhelmed by defenders, forts, militia etc. But in the modern era naval supremacy decisively counters that advantage by letting the mainland invader deploy a generally larger army where they please and above all by cutting off now-essential outside trade and support.

But, for this to even be a question of naval power first the island has to be far enough away from the mainland for artillery to be irrelevant. Venice was an island nation by medieval standards but could be bombarded from the Italian mainland once artillery technology advanced—and that pretty much meant the end of Venetian independence, sooner or later. Britain suffered nazi air attacks that could have knocked out the RAF and thus rendered British surface fleet naval power irrelevant. Today, Taiwan is vulnerable to missiles. So I’d say naval power isn’t enough anymore in the first place. (Although on the flip side, an island with strong artillery, air power, missiles and drones might not need naval protection).

Note: One interesting potential modern counterexample I thought of at the last minute—Ireland’s war of independence against Great Britain. I would have to learn much more but this seems like a good potential example of a nation with naval supremacy failing or being unable (I would imagine for political and cultural reasons) to deploy a navy to bombard ports, enforce a blockade, etc in a war against a smaller island nation sufficiently to defeat it.