IANAG, but you're not accounting for processes that remove salt from the ocean. All of our salt mines come from somewhere -- crust that's been elevated to make an inland sea, that gradually evaporates and leaves a salt deposit. This can then get buried.

Possibly when the tectonic processes stop on Earth, the oceans will continue to get salty from weathering of rocks. And you won't have much addition of water from volcanism, only a little bit from space. But life gets generally hard without active tectonics anyway.