It seems to me the strongest argument above that Sauron should have known about hobbits is the existence of the East-West Road and its importance to travel and intel gathering. However, there are (from Sauron's point of view) numerous enemies along it (various strongholds of elves, men, skinchangers), and after Angmar either little of strategic interest or what there is too strong to immediately attack (ex. Rivendell or Erebor).
Also, one way Tolkien makes Middle-earth work is to have various levels of detail, some deeply gone into, others barely alluded to. Therefore it seems to me the theoretical geography and political geography of Middle-earth could be conceived as much larger then actually discussed in print and seen on maps. Not only to the East and South are there areas where creatures like hobbits might dwell, but to some extent the areas depicted on maps are those that were visited in LOTR. There could be unexplored areas, peoples, polities in such areas as Andrast and the forest around the Sea of Rhun. It's conceivable "Shire" might have been there, in some valleys around the Ered Mithrin, or even in South Gondor. (Sauron might even think the nassty, tricksy Gondorians deliberately created vague legends of halflings living somewhere in the north to dupe him)?
