Why would an elderly person repeat a phrase constantly?

It may be a compulsion or something that soothes him. He may not even be aware of it.

No, he doesn't realize he is saying it. My mom will get caught in a loop of calling me to "turn me over". Sometimes she is in a chair, sometimes I have just repositioned her, sometimes she adamantly denies having said it... and then she says it again as I leave the room. It is one of my hot buttons, it drives me batty, especially when I have tried a thousand different ways to try and figure out if there is something she truly needs.

Sounds like just a habit. Kind of like the person who says "y'know" after every sentence. It is irritating. I used to have habitual phrases when I was growing up. I had to make myself stop saying them. Does your father know he does it? He may be able to make himself stop if he knows it is irritating.

Early in her dementia, my cousin started repeating the same phrase a lot. I thought it was just a habit too, but it continued. I even asked her why she did it, but she didn't know what I meant. Then, at a certain point, she stopped doing it.

He has no idea he is repeating himself. It is very frustrating, and all you can do is change the subject. Pretend you didnt hear it. My aunt did that all the time. You can gently interrupt; say something like, "I'm hungry; are you hungry, Dad?" Comment on the weather, or anything that comes to mind. My aunt would go back to it again and again, and she never knew I had totally redirected her. It wont stop, but you can at least change the subject. I little doubt he will know he was even saying anything. What a devastating and degrading disease this is. I know what you are going through. It's hard. I took care of my mother as well, for eleven years. I made up my mind to never yell at her or degrade her. My brother wasnt so nice, and I finally had to put her in a nursing home. It broke her heart and mine, too. It wasnt the repetitiveness. It was her health.

It is difficult accept their mind is damaged by Alzheimer's Disease

Repetition drive caregivers bonkers.
One wrote; she goes to garage, gets in her car ad just plain screams.