I have a villager who has been nursing the same baby for at least 10-15 years. I don't remember any special potion she took, she is now 50 and her health bar is still pretty full and says "nursing". She was very skilled in research but now she and the baby, I assume are, simply consuming resources (like desperately needed food!) and not contributing to our village.

Will she weaken due to age or stay in this nursing status permanently? Is there any way to hasten her demise so that she's not just leaching off the village?

I had a villager who nursed a baby for a full 24 hours (and I don't recall her having imbibed any colored fluid, either). As with the other reports, she finally relinquished her hold on the baby and went back to her other duties.

You cannot 'terminate' a villager (as much as you'd like to, sometimes). Patience is the only solution in this case.

That's really strange.