There is a limit to how much of a given salt can be dissolved into water, this is known as it's solubility and it's dynamic based upon how much of any particular ion is already present. Once concentrations exceed the local solubility of a given compound precipitation occurs, this can be seen in the modern Mediterranean basin with the precipitation of calcium carbonate onto the seabed. There are also older examples of this response such as chemically precipitated chert in New Zealand.
That's one way in which dissolved chemicals can be re-integrated into the rock cycle, biological processes can also play an important role. Plankton take up many elements from sea water during their life cycle, notably silica and calcite for forming rigid structures these are then deposited in the deep ocean when they and the creatures that predate them die and form the basis for many sedimentary rocks.
So while there is a steady input of mineral salts into the ocean there's only so much of it that can accumulate and in fact a lot of them are removed at far lower concentrations due to biological use and subsequent deposition.
A measure of any deposited material may eventually be subducted with the oceanic crust on which it has settled, at which point it will be integrated into any subductive-melt sourced minerals. There is a trend towards the chemical depletion of the mantle when it comes to certain elements which appears to be a one way street but the ocean does eventually give back a large percentage of what is dissolved into it.