The problem with the Batavian republic is that it was basicly a French puppet state, so assuming revolutionary France or Napoleon gets defeated, the allies will certainly replace its government with the Orange-Nassaus. So yo have a continued Batavian Republic, you need either a surviving revolutionairy France or a succesful Napoleon. The last one is hardly a garantee, as he replaced the Batavian republic with the kingdom of Holland.
Another way is to completely discredit the Orange-Nassua's somehow, so that after the wars the allies don't want them reinstated as rulers of the Netherlands. Not sure if that would do the trick, as they allies were pretty anti-republic, but there is noone else with any claim to the Netherlands.