lord of the rings - Why did Sauron let Gollum roam Mordor freely a second time?

Sauron appears (though this is never said in so many words) to have released Gollum to allow him to hunt for the Ring, in the hope that he would lead Sauron to it. Shagrat seems to be aware of this intentional release:

He's been here before. Came out of Lugbúrz the first time, years ago, and we had word from High Up to let him pass. He's been up the Stairs once or twice since then, but we've left him alone.

(The Lord of the Rings, Book IV, Chapter 10, "The Choices of Master Samwise")

So Gollum has been up and down into Cirith Ungol previously, even after his release, and Shagrat appears to accept this as nothing out of the ordinary. He certainly doesn't say anything to indicate that he notified (or had orders to notify) "Higher Up" of Gollum's appearances.

To understand why Gollum's reappearance near Mordor wouldn't worry Sauron, remember his arrogance, and his assumption that anyone possessing the Ring would behave as he did and try to use it to control others. Sauron had no clue that the Ringbearer would want, much less try, to destroy the Ring.

In addition, the sighting of Gollum by Shagrat's company occurred "early last night" according to Shagrat; that is, the night before Frodo's capture. According to Appendix B, this in turn occurred on 13 March 3019, so that the sighting must be dated to 12 March. This was well after Aragorn's confrontation with Sauron through the palantír, which occurred on 6 March according to the appendix. Sauron was entirely focused, then, on a possible attack led by the Heir of Isildur and therefore presumably coming from Minas Tirith. If anything, he might be more likely to believe that Aragorn had it than to think that Frodo or Sam might. This belief is reflected in the words of the Mouth of Sauron:

"Dwarf-coat, elf-cloak, blade of the downfallen West, and spy from the little rat-land of the Shire..."

If the Mouth of Sauron believed that Frodo was a spy, presumably Sauron did as well; and if he did, it must be because he never considered the possibility that Frodo might be the Ringbearer, intent on destroying the Ring.