We know that Dementors are not immortal creatures, they cannot die as per se, but we know by fact that they can diminish by not sucking fear and souls out of people.
Even though, they are still pretty difficult to destroy and it would be one of the best choices Voldemort would have as a choice for a Horcrux. Is there any evidence in the HP world or any other Potterverse that would give a hint or suggest as to why this didn't happen?
When choosing the objects that he’d use as his Horcruxes, the Dark Lord selected them carefully. As Dumbledore explained, he only used ones that he considered worthy of the honor of holding a piece of his soul, and typically they were objects that had a powerful magical history of their own.
“Lord Voldemort liked to collect trophies, and he preferred objects with a powerful magical history. His pride, his belief in his own superiority, his determination to carve for himself a startling place in magical history; these things suggest to me that Voldemort would have chosen his Horcruxes with some care, favouring objects worthy of the honour.”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
As Valorum mentioned in the comments, Dumbledore knew Tom Riddle as well as it’s possible to know anyone, so Dumbledore is almost certainly right about the reasons behind the Dark Lord’s choices. It’s unlikely that the Dark Lord would consider a Dementor worthy of making one of his Horcruxes - they don’t have their own place in magical history, like the Founder’s objects, nor do they have any significance to him personally, like his diary and Nagini both did - and the Founders’ objects would as well because he felt the most at home at Hogwarts. A Dementor likely wouldn’t be something he’d think worthy, and because of that he wouldn’t want to use one.
