Sulphuric acid alone will not precipitate, but some metals form insoluble sulphates, for example Sr, Ba and to a lesser extent Ca. If you stop a reaction with sulphuric acid, denatured protein may also precipitate. Some organic acids are highly soluble under alkaline conditions, but precipitate under acidic (EDTA is a common example). Without knowing the composition of your assay, it is difficult to give more specific advice.