Sauron knew that the One Ring could be destroyed only in Mount Doom, where it was forged. From Sauron's perspective, no one would think about destroying the One Ring. But if someone did, then Mount Doom would be the only place to do so.
Why did he keep Mount Doom active? Wasn't the risk too high?
My answer here provides the reason; I'll repeat the relevant quote from Of the Rings of Power and the Third Age:
...there was a fiery mountain in that land that the Elves named Orodruin. Indeed for that reason Sauron had set there his dwelling long before, for he used the fire that welled there from the heart of the earth in his sorceries and in his forging; and in the midst of the Land of Mordor he had fashioned the Ruling Ring.
In summary:
In other words, it's wrong to think of Orodruin as being solely connected with the Ring: Sauron had other uses for it too.
Tolkien answered that himself:
"He is in great fear, not knowing what mighty one may suddenly appear, wielding the Ring, and assailing him with war, seeking to cast him down and take his place. That we should wish to cast him down and have no one in his place is not a thought that occurs to his mind. That we should try to destroy the Ring itself has not yet entered into his darkest dream."
Why didn't he destroy Orodruin? Morgoth couldn't do it and he was the mightiest of the Valar. Why should Sauron, a Maia, be able to? I also imagine it may have something to do with its creation by Eru Ilúvatar. Notice that there are very few geographical things are actually destroyed in the mythoi. Even the lands that lie under water still exist, but are difficult to access. :D
I have answered that question here in detail, the answer also got accepted.
I will provide a section from my answer here and include it in this answer:
He 'used the fire that welled there from the heart of the earth in his sorceries and his forging.' The most famous result of his forging, and in fact the only one we know of for sure, was the One Ring.
Mount Doom was much more than just any volcano - Sauron seems to have extended his own power into it, just as his former master Melkor had extended his own power into the flesh of Arda as his means of corrupting the Valar's shaping of the world. In his case, it was probably due to his use of it as a foundry for the forging of the Ring, and was able to control its fires. It seems to have lain dormant when Sauron was away from Mordor, and sprung into life when his power grew.
It's an important place for Sauron as it represents the instrument for his ruling of the world. The more his power grows, the more roaring and fizzing the fires become. We can offer two conclusions. First one, that Sauron's own powers are tied into Mount Doom along with his sorceries. Second one, that he needed Mount Doom for the construction of other items, preservation of his power, form or he was attempting other things with it.
Additionally, we can offer a conclusion that every spawn or forgery of Mount Doom was destroyed or perished with its final eruption...
The world was bent, so that thereafter, only Elven-Ships could sail into the Utter West. Sauron's body was destroyed, but his spirit was not diminished, and he fled back to Mordor bearing the Ring, where he slowly rebuilt a new body and his strength during the time known as the Dark Years. From this point on, he lost the ability to assume a fair shape, and ruled now through terror and force.
...even Sauron's ability to assume any kind of shape or form again.
But while Sauron had much of his former strength, he was still much weakened without the One Ring and remained hidden in the shadows, directing his armies from afar.
Furthermore, we can conclude that he needed it running in order to forge something else, when he grew more stronger, and tie his strength and power into it once more.
The Road approached the east side of the base at a causeway and then wound up like a snake; at that point the Road seemed damaged by the lava and re-repaired several times.
It is also placed deep inside Mordor and thus needn't much protection. He was seeking The Ring with the Eye and flying Nazgul over it as he was rebuilding and wanted to maintain it for himself, only his purposes, whatever they may be. He didn't even consider that someone planned to destroy the One Ring.
"Sauron never considered that somebody would do anything other than try to claim it"
In my opinion, a more phylosophical approach would apply better, as implied by Anthony Grist. A complementary reason for the ring's creation was to corrupt and therefore get valuable information. Sauron in the end represents corruption itself and not necessarily the effects of it. It wasn't even thinkable for it to be destroyed. Who would even dare to think and try to destroy it, apart from an "innocent" and pure hobbit. It is an amazing parallelism of modern society's egoism an concentrated power i.e. political leaderships etc.
Why didn't Sauron Guard Mt. Doom answers this pretty well. He could not conceive that anyone should seek to destroy it. Not to mention the magic of the ring is so powerful that even Frodo could not throw it into the fire at Mt. Doom.
