In addition to the excellent answer by Edlothiad. I think it is worth pointing out that we learn many things reading The Lord of the Rings that were not common knowledge among the people in the books.
At least during the time of the Stewards, the existence of the palantír was a secret. Gandalf says in the Houses of Healing:
Though the Stewards deemed that it was a secret kept only by themselves, long ago I guessed that here in the White Tower, one at least of the Seven Seeing Stones was preserved.
The Lord of the Rings Book Five, Chapter 7: The Pyre of Denethor
Page 856 (Single volume 50th Anniversary Edition)
It is likely that even in the time of the Kings, knowledge of the palantíri was not widespread. When King Telemnar and his children died, and his nephew Tarondor succeeded him and moved to Minas Anor, he may not have known about the palantír until he had time to read his uncle's papers.
Once he learned of it, he may well have thought it of minor importance. After all, Sauron's power was immense, and the additional ability to see events far away (rather than waiting for spies to report them) would only be a small increase in his power. He would not have considered the existence of another palantír in Minas Anor to be a problem, because all he had to do was not be stupid enough to use it.
As suchiuomizu points out in a comment (thanks, suchiuomizu), Unfinished Tales has a section on the palantíri. That section starts out by explaining that the palantíri were not a matter of common knowledge.
The palantíri were no doubt never matters of common use or common knowledge, even in Númenor. In Middle-earth they were kept in guarded rooms, high in strong towers, only kings and rulers, and their appointed wardens, had access to them, and they were never consulted, nor exhibited, publicly. But until the passing of the Kings they were not sinister secrets. Their use involved no peril, and no king or other person authorized to survey them would have hesitated to reveal the source of his knowledge of the deeds or opinions of distant rulers, if obtained through the Stones.
Unfinished Tales Part Four, Chapter III: The Palantíri
Page 403 (Houghton Mifflin 1980 hardback edition)
That paragraph does mention that the palantíri had wardens, who presumably should have tried to keep the palantír of Minas Ithil out of Sauron's hands. We do not know exactly what happened, but we are told that:
Two things contributed then to the neglect of the Stones, and their passing out of the general memory of the people. The first was ignorance of what had happened to the Ithil-stone: it was reasonably assumed that it was destroyed by the defenders before Minas Ithil was captured and sacked; but it was clearly possible that it bad been seized and had come into the possession of Sauron, and some of the wiser and more farseeing may have considered this. It would appear that they did so, and realized that the Stone would be of little use to him for the damage of Gondor, unless it made contact with another Stone that was in accord with it. It was for this reason, it may be supposed, that the Anor-stone, about which all the records of the Stewards are silent until the War of the Ring, was kept as a closely-guarded secret, accessible only to the Ruling Stewards and never by them used (it seems) until Denethor II.
Unfinished Tales Part Four, Chapter III: The Palantíri
Page 403 (Houghton Mifflin 1980 hardback edition)
So it appears that the palantír of Minas Ithil was captured when Minas Ithil fell to Sauron. There is no reason to suppose that the defenders were indifferent to its capture, but they presumably had other things on their minds at the time. At least some of those who knew of its existence understood that it may have been captured, but they didn't consider it a major setback.