Otherwise you can have HCO3- ions which could keep Ca++ ions in solution (if I remember well). Boiling the solution eliminates dissolved CO2 and so H2CO3 and HCO3- ions.
In the presence of excess sulfuric acid HCO
3- won't survive long enough in the solution.
Besides, I think you may be mixing two things - HCO
3- doesn't 'keep' Ca
2+ in solution, but Ca(HCO
3)
2 is much better soluble in water. Thus water kept over solid CaCO
3 will have higher concentration of Ca
2+ when saturated with CO
2.