Why didn't Sauron feel the Ring?

I would say it was the fact that both Pippin and Aragorn looked into the "seeing stones". This forced Sauron to focus his "eye" on the west. He didn't trust Saurman and felt he was being betrayed by him when he mistook Pippin as the ring bearer and then when he saw that the King of Gondor was alive and using His Stone it forced him into action in a "too hasty manner", as Treebeard would say!!