Why did Sauron fear Aragons coronation?

[Inziladun]

One thing I find curious that may bear on this is Aragorn's statement to Frodo on their meeting at Bree.

'I did not intend to tell you all about myself at once. I had to study you first, and make sure of you. The Enemy has set traps for me before now.'

That suggests that Sauron was worried enough about the idea that an Heir of Isildur remained to have in some way been looking for evidence of such a person. Aragorn, of course, does not elaborate on the "traps", but it says something that even before the War of the Ring the Heir of Isildur was on Sauron's mind.

[Aiwendil]

Originally Posted by Inziladun

That suggests that Sauron was worried enough about the idea that an Heir of Isildur remained to have in some way been looking for evidence of such a person. Aragorn, of course, does not elaborate on the "traps", but it says something that even before the War of the Ring the Heir of Isildur was on Sauron's mind.

Possibly. But Aragorn was also the Chieftain of the Rangers; and even if Sauron had no idea that an heir of Isildur was alive, he must have been aware of the existence of the Rangers of Arnor. So it may be that the traps Aragorn refers to were set merely against the commander of the northern Dunedain, with no particular thought that he might be a claimant to Isildur's throne.

[Inziladun]

Originally Posted by Aiwendil

Possibly. But Aragorn was also the Chieftain of the Rangers; and even if Sauron had no idea that an heir of Isildur was alive, he must have been aware of the existence of the Rangers of Arnor. So it may be that the traps Aragorn refers to were set merely against the commander of the northern Dunedain, with no particular thought that he might be a claimant to Isildur's throne.

Would Sauron really have been that concerned about the Rangers, though? It doesn't look like he had any regard for Eriador in the Third Age, until he learned that was where his Ring had probably been taken. And if he or his servants knew of the Rangers, he should have observed they were guarding the Shire, and he shouldn't have been so clueless either about the location of Hobbits there.

[Zigûr]

But before Aragorn used the Palantír do we have any indication that Sauron was concerned about an Heir of Elendil?
That being said it seems to me that Aragorn's activities as Chieftain of the Northern Dúnedain, as Thorongil in Rohan and Gondor and his adventures in Rhûn and Harad must not have gone unnoticed even if Sauron wasn't aware of his lineage.

[Galadriel55]

I think that Aragorn was referring to more general traps, against a Numenorian warrior brave enough to stick himself in Sauron's path. I doubt those traps were even aimed with the same person in mind, or for a greater purpose. They're just traps.

As for Sauron apprehending the heir of Isildur, I don't think he thought him dead as much as lost. I think he wasn't fooled by the destruction of Arnor into thinking that Isildur's line ended, but since the heir did not show a sign for so many generations he probably thought that the lineage was forgotten, or lost, or too mixed. He was still wary of a potential heir, or a Dunedain leader with enough lineage to be proclaimed King, but not as much as he would have been had he known the truth about Aragorn (which he became after he saw him in the Palantir).

[Andsigil]

Many competent generals waged war against Sauron over the millenia; some of them more formidable than Aragorn.

I've always thought that Sauron feared Aragorn's coronation as a sign of great change more than he feared Aragorn storming his gates.

[Inziladun]

Originally Posted by Zigûr

That being said it seems to me that Aragorn's activities as Chieftain of the Northern Dúnedain, as Thorongil in Rohan and Gondor and his adventures in Rhûn and Harad must not have gone unnoticed even if Sauron wasn't aware of his lineage.

A line from the Unfinished Tales section The Hunt For the Ring could contradict the idea of Sauron being interested in Aragorn personally.

It would then no doubt be in April before Sauron heard that Gollum had been seen again, apparently captive in the hands of a Man. This might mean little. Neither Sauron nor any of his servants yet knew of Aragorn or who he was.

That would seem to indicate that Sauron and his servants were simply vigilant for signs of an Heir of Isildur's return, though as Aragorn noted after his partial reveal to Sauron, the latter probably in his heart believed it wouldn't happen.