can your villagers die because of old age?

yes.

actually, the only villagers I've had to die, died from old age.
All were at least 68 (in earlier part of game), oldest was 80.

Yes, and old age varies depending on what level of medicine tech you have. If you are still on level one, it can happen in their mid 50's....if you're on level 3 they can live into their 80's. The person will move much more slowly and when you click on their details, it will say "Elderly" where everyone else's says "Healthy". This means they are close....

actually, the villagers can live into their 90's or above if u study the cactus and put them in the garden. also, if u make them eat the magical fruit from the strange plant in the back (the lumpy one) then it prolonges their lifespan.

yes they cane die of old age