Older hens have a variety of issues that can come up. Breeds that lay a lot of eggs are considered old at 1-2, as this is when reproductive problems like infections, internal laying, water belly and other conditions can occur. The fact your hen is 6 means she's been doing great!
I would suggest a few things to help her:
Offer a warm, comfortable place to perch. Perhaps a wider area so she doesn't have to balance as much. A heat light can help during the winter.
Don't encourage laying. Don't keep a light on during the night for her as this will only tire out her body more.
Provide oyster shells, vitamins in her water or on her food, and lots of nutrient rich treats like scrambled eggs, she'll love this
Make sure she has easy access to her perch (small steps or a ramp so she doesn't have to jump) and can easily get to her food and water
Make sure the roosters aren't bullying her
You can also keep in mind that hens during the autumn often seem sick as they enter molt. The eggs will be in worse condition, the hens will walk in a tired fashion and be reluctant to come off their perches or run or try to fly. I've thought my hens were dying sometimes they were so uncomfortable during the molt. Once this passes, hopefully your girl will feel better.
Best of luck!
