I am going to answer the question without reference to books or the internet. I think I can do this because there is a common sense element to this question. Disagree? Tell me. Don’t hold back! The problem is inherent in the human to cat relationship. We are different species with very different habits. Humans often don’t really grasp this.
Not all cats meow incessantly at night, most don’t in fact. There is more than one reason why a cat won’t stop meowing at night. However, a major reason is because at night humans go to bed and sleep while cats are designed to be active. Or at least the domestic cat has inherited the wild cat ancestor’s motivation to hunt at dawn and dusk and in fact at anytime in the night. Domestic cats also hunt in the daytime. But the key issue is that cats don’t treat nighttime as a time to sleep. If anything cats are likely to be more active at night than during the daytime.
Therefore, at night when their human sleeps the cat is alone. Abandoned. Her human companion with whom she has interacted throughout the day (ideally) has disappeared and apparently wants nothing to do with her/his cat. This condition is exacerbated if the cat is kept indoors full-time. In fact I’d suggest that if a cat is meowing at night all the time it is more likely that she is a full-time indoor cat as she could entertain herself outside by hunting.
As the cat wants to be active she may call out and make demands on her human caretaker/guardian. She wants something to happen. She is alone and somewhat confused by the strange behaviour of her human companion who she treats as a cat (in my view).
A cat meowing at night may be compounded by the cat’s owner closing the bedroom door at night to keep her cat out of the bedroom. Her cat wants to be in the bedroom and makes a fuss when she can’t get in. Cats do meow to make demands on people. It is said that the meow has been formulated to talk to people. Cat-to-cat interactions don’t contain meows. So the meow is a demand; a demand to be allowed in the bedroom and a demand for the human to be active and do something.
So that, for me, is the main reason why your cat won’t stop meowing at night. Cat behaviourist will say that the response from the human should be to not respond to the cat’s demands. I disagree. I think it is unfair and it won’t resolve the problem; although it might in time. The solution is to allow the cat to entertain herself outside in an enclosure or through free roaming (which may be impractical). Adopting another cat might do the trick but there are some possible problems there too.
I’ll suggest something controversial: buy a Thundershirt and put it on your cat at night. He/she will calm down, be more sleepy and probably sleep with you on your bed (and get in the way of your sleep that way!). Note: this product has varying levels of efficiency depending on the individual cat.
Another reason might be because your cat is old and has some dementia. Under these circumstance she/he may become confused at night when ‘abandoned’. She may yowl and howl in her confusion.
If your cat is not spayed she may caterwaul – a call for a mate. But I’d expect this to be unusual. I’d hope that the vast majority of cats are spayed and neutered.