Maddy wrote to Downing Street expressing her concern for the future of West Cumberland Hospital in Whitehaven, where she was treated for pneumonia.
Some services have been moved from the hospital and others are currently under review.
Maddy said she was excited to receive a reply, in which Mr Cameron said such decisions were taken by local doctors.
She had appealed to the prime minister to “keep our hospital open” and to “write back” – and was rewarded with a written reply.
Maddy told BBC Radio Cumbria: “It was really exciting when I saw it on the mat.
“But there was one problem with the letter. He didn’t really answer my question.”
In her letter Maddy said she was concerned some services had been moved to Carlisle, nearly 40 miles away, and the hospital would lose its consultant-led maternity services, which are under review.
Mr Cameron said in his reply: “It is very important that we have good local health services so that people who are sick can get the very best care quickly.
“That is why four years ago we gave £70 million to West Cumberland Hospital to improve its services.”
This was a reference to some capital funding the hospital secured from the government in 2010.
“Decisions on local health services are taken by local doctors as they know what is best for your area,” the letter went on to say.
The future of services at the hospital will be decided by North Cumbria University Hospitals NHS Trust.
Her mother, Emma Gooch, who is part of a campaign to save services at the hospital, said she was pleased Mr Cameron had taken the time to write back to Maddy.
But she criticised the substance of the letter, saying the prime minister “just evaded all questions”.