The reason Ti is rumored to last the longest is that Ti is twice as flexible as steel, so bending moments that might go past a steel tube's elastic limit will still be well within Ti. For this reason, Ti is a real pain to cold set - you have to bend it much farther for the bend to remain. It is essentially more "rubbery" than steel, but can be oversized to similar stiffness.
That advantage is also true in directions where carbon fiber is typically not strong - like side impacts on the tube. A good wack on a top tube may make a bigger dent or bust a CF tube, but will leave less of a dent on Ti.
That said, Ti is the most sensitive bike material to welding cleanliness (but not to heat cycles), so most Ti failures come from polluted welds. You'll virtually never see a Ti frame that failed nowhere near a weld or Heat Affected Zone where a nugget of oxide formed in the metal. But I've seen plenty of steel bikes where riding work hardened and cracked the chainstay well away from the BB.
For a bike that is pleasantly flexible rather than ultrastiff, Ti will take more work cycles and impacts than other materials. But any frame that is stiff or thick enough will last even longer - it just won't be pleasant to ride.