The Ottomans were the superpower of the Mediterranean world and skill and good fortune were really the only things that kept them from spreading further into Europe. Is there any point from 1500 to around 1850 that the city could realistically be reconquered by a European force and if not what POD do you think would work? My initial thought is that a less severe Reformation leads to a more politically united Europe and further crusades.
There's no point in OTL when Christian reconquest was "near-plausible", but there are points where the general current could have switched direction, such that it could have happened.
For instance: suppose better leadership for Hungary at Mohacs, leading to a decisive Hungarian victory, with the Turkish army annihilated and Suleiman dead. Then if Hungary has some more good leaders, a series of campaigns leading to the City doesn't seem out of the question.
This does invite a question, though. The Ottoman state was enormous, far larger than any in Europe except possibly Muscovy or Poland. Despite several grossly incompetent rulers like Selim the Sot, Turkey maintained control over Asia Minor, the Levant, Mesopotamia, Egypt, Bulgaria, Greece, Albania, Bosnia, Serbia, Wallachia, Moldavia, Crimea, Transcaucasia, and Hejaz. How did they do it? How did the Ottomans twice lay siege to Vienna, while no European army came near Istanbul for centuries?