The Ring and Its GPS Tracker

[mormegil]

Originally Posted by Inziladun

It just seems to me that if Sauron could have had the awareness he obviously had of Thráin's ring, and the ability to get it from him, he should have had some inkling at least that The One still existed, and had not been destroyed.

If I remember correctly, and hopefully this is not just the movies, but I don't believe Sauron ever believed the ring would be destroyed. So he always knew it was whole and believed it unfound; Your question is pertinent however and it would seem that perhaps the ring did not send a signal sufficiently strong for him to locate it.