Why does a reaction stop when turning into a solid?
The reason is due to the surface area of calcium carbonate available to react.

When reacting a block of solid calcium carbonate with dilute sulphuric acid, solid calcium sulphate is produced which is deposited on the surface of the calcium carbonate block (since that is where the reaction occurs). The calcium sulphate is insoluble in dilute sulphuric acid and so you end up with calcium carbonate coated in a layer of calcium sulphate, which stops the acid from getting at the carbonate and so stops the reaction.

In contrast, calcium nitrate, produced from the reaction with nitric acid, is highly soluble in dilute nitric acid and so no solid layer forms around the carbonate block and the reaction can continue until one of the reagents is used up.