Unhappy with Her Increasing Dependence

Today is my Mom's birthday. While we're celebrating another year, she's unhappy about her increasing age.
It's not that she's not happy to celebrate her birthday. It's that she recently said she feels like she's always asking us for help and it's not going to get any better as she gets older. She said she doesn't like asking for help and doesn't like knowing that she's going to do it more and more in the coming years.
I reminded her that she and Dad helped us tremendously through the years. When our girls were little she'd cover over every week to watch them for the time between when I left to teach class and Daddy came home from work. When I sprained my ankle and ended up in a soft, boot cast Dad drove me to and from class so I could continue to teach. Dad came over whenever we had a house problem that needed his expertise. I cannot remember the number of times I called Mom to say, "I have to take one twin to the doctor. Will you please come over and watch the other one?" Of course she always did.
I know both my brothers could create their own lists. Mom and Dad were always available to help. This does not make my Mom feel better.
For her asking for help puts her in the same, dependent category my grandmothers were in when we were growing up. Many weekend days were spent going from Gram to Gram to mow the lawn or shovel snow or do some other house project. This fell to us because we were the only relatives in the area. Everyone else moved away.
As the grammas got older it because more about doctor's appointments and hospital visits and grocery shopping than anything else. Mom made weekly visits to see her mother long after her mother had forgotten that Mom was her daughter. We offered to split the visits, but Mom always said it wasn't our responsibility.
She sees herself as becoming a burden and that doesn't sit well with Mom. She was independent long before the women's liberation movement, which she never supported. She used tell stories about women chastising her at her desk when she became a bank officer. You'd think these women would be happy to see another woman rise through the ranks, but they always lamented that she was letting down other women because she had "Mrs." on her nameplate. Even within a movement to give women more freedom she was an independent.
I realize we cannot make this better for Mom. I wish we could convince her that she's not a burden, but I'm not sure we can. For now we can just be as casual as possible about helping her until she finally accepts that none of us can do it without each other.