> for each entity have a separate class to provide the database access

Let me correct you: for each entity that needs database access. This is why I'm talking about layers here: sometimes entities are never persisted directly, but only as "parts" or "relations" of other entities; in other cases you might have a very complex persistence implementation (e.g. some entities are stored in a RDB, while others in a filesystem) and there is no clear mapping.

I recommend you to approach this from the perspective of each domain entity individually; "persistability" is essentially just another property which might or might not apply in each case.