In fact, J.R.R. shed some light on the subject of the future of hobbits in the Fourth (or is it Fifth?) Age:
"The much later dwindling of hobbits must be due to a change in their state and way of life; they became a fugitive and secret people, driven as Men, the Big Folk, became more and more numerous, usurping the more fertile and habitable lands, to refuge in forest or wilderness: a wandering and poor folk, forgetful of their arts and living a precarious life absorbed in the search for food and fearful of being seen; for cruel men would shoot them for sport as if they were animals. In fact they relapsed into the state of 'pygmies'."
These lines always make me feel sad.
