Gandalfs Beard wrote:the special protections for the Shire would have faded with them.
The Shire didn't really have any special protrections, just remoteness and a band of Rangers looking after the borders. Of course, these would eventually fade as the Reunited Kingdom passed away (eventually) and other populations (mainly human) increased.
As for Hobbits, they are generally uncomfortable around humans, with the obvious exception of the Bree-land ones. The Prologue to LotR mentions that Hobbits and Humans have undergone estrangement though, and the first chapter of The Hobbit makes mention of their timidity around humans. Granted, it is possible that these references to latter-day Hobbits are relevant to only a portion of the original population, but I can think of no evidence for interbreeding. I can think of even less to suggest that the xenophobic Dwarves engaged in any significant interbreeding. I bow to your knowledge about breeding and concede that it is theoretically possible, however.
It's a bit depressing, but I think that the Hobbits and Dwarves merely dwindled and possibly died out, though perhaps there are still a few hiding out somewhere....
