Do I take the teddy bear away or continue to let her care for it?

I would reassure her that the baby is just sleeping and she has to calm down or she will upset the baby.

My grannie loved her baby doll and we always put her down for her nap so we could cruise around the NH and visit. We bought new clothes, changed her diaper when it got saggy from to much loving and made a fuss about how big she was getting, just like a real baby. It worked and grannie was satisfied that all was well when we went cruising.

No you don't take her teddy bear away, as she finds great comfort and joy taking care of it. Many people with dementia(women in particular)love to carry around a baby doll or in your aunts case a teddy bear, and love on them, and care for them. You will see that a lot if you were to ever visit a memory care facility.
I think it's quite sweet to see, and it does no one any harm.
Perhaps next time she says that it has died, you can just go along with things and tell her that you will try giving it mouth to mouth, or that you will take it to the doctor.
Bless you for looking after your aunt.

I wish my hubby had a teddy bear. He is currently fixated on a long-handled shoehorn. He carries it with him and frets if he sets it down and forgets where it is. He actually sleeps with it clutched in his hand.

Mom’s been sleeping w a big stuffed beagle since my dad passed. When she moved to AL i replaced it with a clean one. She also really enjoys her beanie babies. She has a sofa arm tray with pockets for glasses, nail files, etc. and the tray on top holds her pens and snacks… then she discovered that the beanies sit nicely
up there and are close so she can hold them and talk to them. They make her smile and laugh. She often says ‘ Have you seen this? His big eyes are so funny.’ ( i pretend they are new to me even tho i brought them awhle back) So very thankful her level of dementia has made her childlike and happy alot with simple things like toys, ice cream, hersey kisses and bananas.

I use to work in the central office of a company that owned multiple NHs. My job was in multiple areas of management from controller to maintaining and updating computers and the Medicare/Medicaid software. Often when I was walking down the halls just to do an examination of the rooms/facilities, I would have a lady walk up to me and hand me her doll. I would cradle the doll like it was a baby, rock it a little and talk to it. The smile on the residents face could make my day. Another time a lady asked me if I could help her find her dorm. She thought she was back in college, somewhere in Missouri. A nurse overheard and whispered which wing and room number. I walked her back all the while asking about her family. She said she has to go back from time to time and help her family on the farm. Got her to her "dorm room" and said my goodbyes. I came to believe if you are going to deal with dementia, what better way than to regress to a happy time. Not an expert, but it seems to me that whatever world they are in is better than being confused and upset. If its manageable and doesn't disrupt others, let her have the "baby". When she becomes upset and thinks it has died, you're going to have to be inventive. Assure her the baby is fine. It may take some time to figure out the best way to assure her. But taking the baby away isn't a good idea. For my sister in AL, sometimes she thinks she is part of the staff, sometimes she thinks she is going to be interviewed for a job. She has a master's degree in psychology and worked as a family councilor. Served in the Army as a sergeant so she has a lot of flashes of a past life that she seems to relive. I just talk with her like she is what she thinks she is as long as its not troublesome to others. Find a way to assure her the teddy bear is ok. Where ever she is living in her mind, let her find some comfort and happiness in her last years. I'm sure most of the other answers will tell you the same.

I’m glad she finds joy with the bear. That’s a gift for you both. If she becomes distraught say something like “no silly, she’s napping, you know babies sleep deeply” and distract her. Hopefully she’ll be satisfied and move on

Never, never take the bear away. Reassure her that he's fine, but never take that connection away from her. There will be fewer and fewer connections for her as time goes on, and the bear may be the last one she keeps.

SOMETIMES illogical situations need illogical remedies.

Pretend calm concern and put your head on teddy's chest. Tell her it's not dead but instead in a non-lethal coma which is good for neurological repair.

Wrap teddy's head with a short ace bandage and in a whisper tell her that it was a good thing she discovered the situation in time. You could ask her if she thinks a blanket may be helpful.

After awhile, take off the bandage, and let her rewind it, or just take it off when she's not looking and stash it for the next time.

I don't have the exact same experience but depending on the day I've told my husband brief eye-crossing whoppers just to take his worries away.

I hate, hate doing that. It's very uncomfortable, but if it works what the heck. It soothes bad situations and saves time and nerves.

G-d how I miss adult interaction.

Your aunt is using the teddy bear as a tool to express emotions that she is feeling. Sometimes they will be sad emotions because she is feeling sad. She's allowed to feel sad, isn't she?

When she is, are you able to console her? You could try developing the conversation to explore what else might be involved in these thoughts and feelings, but dig gently!

No, don't take this object of comfort away.
Grandma1954 has another good idea, but she may still prefer her teddy bear. If she does have times when she cries over the bear and what she imagines it is only to provide her comfort, to tell her you are sorry, ask her if there is anything you can do, comfort her.
Do know that for her this is very real. Taking it away would likely be very painful for her. It was the opinion of Oliver Sack who lifelong studied the mind, that their worlds are very real, just so different and alien from our own that we can't understand that. So our deficits are perhaps as severe as hers? Many things are beyond explanation and understanding. This is but one of them.