Any ideas on what I can say or do when they are repeating like a broken record?

Answer every time.
Answer every time.
Answer every time.

Oh, sorry. Repetition can be absolutely crazy-making. Yikes! But it may help to remember that she can't help it, she isn't even aware of it, and, sigh, there is no way to "cure" her. And take some consolation that this behavior will probably go away on its own (after what will seem like an eternity).

Sometimes a distraction helps. Change the topic a bit. "Your home is lovely. What is your favorite part of the house?" ... "The new furnace isn't in yet. You can go home after that. For now, let's go into the kitchen and have a snack. Do you want graham crackers or a pear?" "Perhaps tomorrow you'll go home. Today would you help me match up the socks that just came out of the drier?"

You will notice a lot of similarities in the first three answers here. That is often a clue that the experience is common and you are hearing the result of some trial-and-error-and-trial-again. Experience is the best teacher -- and somebody else's experience is cheaper and easier!

SarahLee, when someone with memory lost says "I want to go home", they usually mean their childhood home, back with life was fun and not so complicated.

My Mom use to ask to go home, at first I thought she meant the house she shared with my Dad [Dad was still at the house], but Mom lived in long-term-care as she needed a much higher level of care. Anyway, she started to give me clues that connected me to her childhood home many States away. Then she wanted to visit her sisters and her parents. Oh dear, my Mom was 98, thus no parents and her sisters had all passed on.

Thus, any time my Mom asked to go home, I would say "maybe tomorrow" and she would smile, and within the hour she had totally forgotten about "home", until the next day.

I would recommend reading a lot about dementia and also viewing the Teepa Snow videos on Dementia on You tube. She has so many good tips and explanations about dementia behavior. It's been very helpful for me, though, I don't care for my LO in the home.

From my experience with my LO, the repeating was mainly done in a stage and while it was extremely prevalent at one point, as her dementia progressed, it faded away.

As you already know, there is no real way to prevent the repeating, because the person forgets what they have just said and what you have just said. Reminding them that they are repeating is really not helpful.

I used to pretend that I was in a contest to see just how many times I could answer the same question in one hour. So, I would answer her question over and over, until she got tired or moved on. It can play havoc on your nerves. I don't have any suggestion, except to take breaks and get respite care for your own mental sake. AND try to distract the person with dementia. If you can change the subject, keep her mind focused on some activity or ask her questions, so she doesn't have time to focus on the same question or comment. Some try folding clothes, playing music, holding a doll or stuffed animal, etc.

It's a personal decision, but, I never saw any point in telling someone that they were not going home. I tried to make my LO happy and said whatever worked in the moment, because what I said would not be remembered anyway. So, some people say, you'll go home when your doctor signs off on it or when the heater gets fixed, etc. If it satisfies their mind, then, I don't see the harm.

I'd also discuss the matter with her doctor. Sometimes dementia patients are overly anxious and may suffer with mental distress. Medications may offer relief. Meds helped my LO quite a bit in helping her relax and be more content.