It's certainly most often used to describe the character or behavior of people or animals, but I found an example in the Oxford dictionary where it was used to describe a legend: "a tenacious local legend"

Tenacious can be a disease. He suffers from a tenacious cancer. The child can have a tenacious fear of darkness. The mold was tenacious and had to be eradicated with an industrial cleaner.

It's a good question. Here's another example. From the Collins Cobuild dictionary: "Definition: If you describe something such as an idea or belief as tenacious, you mean that it has a strong influence on people and is difficult to change or remove. [Example] ...a remarkably tenacious belief that was to dominate future theories of military strategy. " Your question asks "can" we use it to describe things (not people/animals). So we now have (with the other answers) several examples of the word being used in a similar sort of context. "Can" we use it for other things also? That depends on your definition of the word "can". I'd say "Why not?" For example, if someone says "There's a really tenacious stain on this." this sentence would probably communicate what the person wants to communicate. It is probably more likely that people would say "stubborn stain", but only because it's a collocation. There's no rule that says you must say "stubborn" not "tenacious"

Words with strong Latin roots, like "tenacious", hold on to those roots tenaciously. Their meaning varies little over time because the root anchors their meaning. There! I have just given you an example of "tenacious" applied to a non-living thing.

of several dictionaries this one https://www.collinsdictionary.com/dictionary/english/tenacious gave some very good alternative definitions other than a tenacious person. ADJECTIVE 1. holding or grasping firmly; forceful a tenacious grip 2. retentive a tenacious memory 3. stubborn or persistent a tenacious character 4. holding together firmly; tough or cohesive tenacious cement 5. tending to stick or adhere tenacious mud The most tenacious characters are female. Times, Sunday Times (2008) The actor himself had a similar brush with mortality and a similarly tenacious grip on life when an accident almost ended it. Times, Sunday Times (2007) His memory was tenacious, and he excelled in argument and repartee. Christianity Today (2000) He emerged as a tenacious interviewer, who was not in awe of anyone. Times, Sunday Times (2013) Has a reputation for being firm but fair, tough and tenacious but as she finds. Times, Sunday Times (2010) Both worked their way up through the ranks, both are energetic, stubborn and tenacious and both are enjoying an impossibly bright twilight to already distinguished careers. Times, Sunday Times (2013)