The Great Siege didn't work out but one would think that given the crucial strategic position of Malta, the Ottomans would have made another attempt at a later date.
Why didn't that happen?
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Suleiman the Magnificent died a year after the Great Siege and was succeeded by Selim II. The change in leadership also brought a change of focus. Selim decided to move against the equally strategically positioned Mediterranean island of Cyprus.
The War of Cyprus started only five years after the Great Siege, and although the Ottomans ultimately prevailed, the bulk of their fleet was destroyed in the Battle of Lepanto. This was the first naval defeat for the Ottomans since the 15th century, and although they quickly replaced their lost ships, the ~20,000 experienced seamen lost in the battle weren't as easy to replace.
Despite this, the Ottomans captured Tunis with relative ease only three years later, and only a year after they secured Cyprus. Their attention turned away from the Mediterranean, and towards Austria (Long War) and Poland (First & Second Polish-Ottoman War) in the West and Safavid Persia in the East (1578–90 & 1603–18). The following years, a very long series of minor internal and external conflicts demanded immediate attention and resources; the Empire had already entered its stagnation phase.
It could be argued that the main reason the Ottomans never tried to besiege Malta again was that after 1565 they never actually stopped being engaged in one war or another. At the same time though, up until the 1630s their dominance in the Mediterranean was undeniable, even with the bulk of their fleet engaged elsewhere (or rotting in Istanbul). They managed to capture Madeira (1617), raid western England and reach as far as the shores of Sweden, with little - if any - resistance. Malta's position turned out to be quite less significant than both the Europeans and the Ottomans thought in 1565.
Furthermore, sympathy - and gold - poured into Malta from all over Europe after the Hospitallers' sensational stand against the Ottomans. Fort Saint Elmo was not only rebuilt, but integrated to a fortified city; Valletta. If it had taken a month for the fort to fall in 1565, with the new fortifications it would be a nearly impossible task for any assailant. The Ottomans had already suffered two humbling defeats, in Malta and in Lepanto, besieging the reinforced island that was proving in practice to be tactically insignificant simply didn't make sense.