There's a fairly good tactical reason for this, at least from Sauron's perspective.
There's evidence that Sauron is withholding his forces, which we later learn is in preparation for the attack on Minas Tirith. In The Two Towers, Morgul orc-captain Grishnákh reveals why the Nazgûl are no longer searching for the Ringbearer:
'But the winged Nazgûl: not yet, not yet. [Sauron] won't let them show themselves across the Great River yet, not too soon. They're for the War – and other purposes.'
The Two Towers Book III Chapter 3: "The Uruk-Hai"
Considering the singular importance of the Ring to Sauron, the fact that he won't devote even one of his most powerful servants to its search (to say nothing of the fact that he's outsourcing the operation to an ally he doesn't complete trust) suggests that he's keeping his forces on a tight leash.
The other thing to remember is that Sauron doesn't expect the Ring to be taken to Mordor. As Gandalf says in Fellowship:
Into [Sauron's] heart the thought will not enter that any will refuse it, that having the Ring we may seek to destroy it.
The Fellowship of the Ring Book II Chapter 2: "The Council of Elrond"
It's clear that Sauron expects the Ring to be used against him, and the logical place for it to go is Gondor, and Minas Tirith specifically.
Then Aragorn and Boromir have the following exchange in Fellowship:
'If the Emyn Muil lie before us, then we can abandon these cockle-boats, and strike westward and southward, until we come to the Entwash and cross into [Boromir's] own land.'
'We can, if we are making for Minas Tirith,' said Aragorn
Fellowship of the Ring Book II Chapter 9: "The Great River"
All of this suggests to me the following:
- Sauron has some awareness of the movements of the Fellowship; he knows that they're travelling south along the Anduin
- Sauron expects the fellowship to head for Minas Tirith, and the best route is south-westerly from the Falls of Rauros
- Since he does not expect the Ring to head east from the Anduin, which is the path to Mordor, it doesn't make sense to allocate his resources to defending it.
This isn't an out-of-character move for Sauron, as Gollum points out in The Two Towers:
'Hobbits must see, must try to understand. [Sauron] does not expect attack that way [via Minas Ithil and the pass of Cirith Ungol]. His Eye is all round, but it attends more to some places than to others'.
The Two Towers Book IV Chapter 3: "The Black Gate is Closed"