John Alleman, 52, was the second unpaid mascot to die in the past two years.
He collapsed while waiting at a bus stop in front of the diner last week and has been taken off life support.
The medically-themed diner is famous for its huge hamburgers, extra-fat milkshakes and chips cooked in lard.
It uses the slogan: "Taste worth dying for."
Owner Jon Basso said Mr Alleman went to the restaurant every day and encouraged passing tourists to try its offerings.
He said: "He never missed a day, even on Christmas.
"People just loved him. He connected with people in a real way."
Mr Alleman became an unofficial mascot for the restaurant, which features waitresses in nurse garb.
His caricature as Patient John graced its merchandise and menus.
Mr Basso said Mr Alleman weighed about 13 stones and his death showed heart attacks can happen to anyone.