When an iodide/iodate solution is acidified with H2SO4 instead of thiosulfate, why should it be titrated immediately?
After acidification with $\ce{H2SO4}$, starch starts to hydrolyze to its component sugars. Lugol's iodine does not react with those sugars to form the blue complex.

Our amylose is gone, today,
Its trace we'll see no more,
For what we thought was $\ce{H2O}$
Was $\ce{H2SO4}$.