This is just speculation, but it feels like being sick drains your health gradually, while eating Sauge and the rest of the foods that make you feel stronger combats that by regenerating your health gradually, which may or may not outpace the drain. However, if you can't sleep comfortably, the maximum amount you can heal up to takes a hit and you see your health bar stopping recovery further and further from your actual max health. To fix that you'd want to sleep on a bed or a bedroll while the temperature is at 15 or higher, then eat a Sauge when you wake up.