I am currently working my way through The History of Rome podcast, and in the segment about the first Punic war it is mentioned that after the failure of Regulus raid, the Roman fleet arrived in the spring to pick up the survivors. On their way home a storm blew up and reportedly sank the vast majority of the fleet, causing 80,000+ casualties. There seems to be numerous other occasions in antiquity involving the total catastrophic loss of fleets due to storms, navigational errors, etc.
When did technology and techniques advance to the point where history stops seeing these massive near total losses of fleets?
There's not really a single point where technology "advanced" to make disasters impossible, because ships are crewed by humans, and humans make pretty terrible decisions sometimes.
There's a rather large cruise liner that was only recently hauled off a rock off the Tuscan coast, for example, which I will not go into further due to the 20-year rule. During the period I study: in 1800 the first-rate battleship HMS Queen Charlotte caught fire and exploded, killing 673 men, for reasons that are not entirely clear but may be related to bunting thrown over a match-tub. The Action of 13 January 1797 resulted in the destruction of two ships -- one large French ship and one British frigate -- as the result of accident. (The British navy during the entire period of the French Revolutionary and Napoleonic wars lost more ships and men to accidents than to enemy action.) HMS Victoria collided with HMS Camperdown in 1893, sinking Victoria, as the result of admiral's orders that no one dared countermand; 358 of her crew died. (A rather famous survivor was John Jellicoe, who would go on to command of the Grand Fleet at Jutland.)
Moving to a more recent century: The worst loss of U.S. ships in peacetime was the Honda Point disaster in 1923, in which nine ships of a destroyer squadron traveling at 20 knots (around 35 kph) ran aground; two managed to refloat themselves but seven were lost, and 23 sailors killed. The USS Missouri, one of the last battleships ever built by the U.S., ran aground on Thimble Shoals on a calm sunny day in 1950; there were no casualties, but the enormous ship remained stuck in plain view of Norfolk for two weeks. The USS Thresher and USS Scorpion, advanced nuclear-power submarines, reached crush depth and sank in 1963 and 1968 respectively, with the loss of their entire crews. The USS Forrestal suffered a severe explosion and fire on its flight deck in 1967, killing 134 and injuring 161 and causing $72 million in damage. (The Forrestal fire was one of three major postwar carrier fires.) The USS John F. Kennedy collided with USS Belknap in 1975, causing eight deaths aboard the two ships. The resultant fire caused Belknap's superstructure to melt almost completely to its deck level. And those are just examples from the U.S. navy, off the top of my head.
I could go on, but I think you probably get the point -- technology is not enough to mean that disaster at sea doesn't happen.