Are you a vampire? Vampires stop generating Stamina when in sunlight, in vanilla Skyrim (vanilla = no mods for that)
You said you don't have a disease, so I guess it depends on if you define vampirism as a disease. I think of it as an asset. I love vampires.
EDIT: sounds like a glitch. However, it's possible that you have a disease and didn't know it. You can check to see if anything is directly causing this by going into your Magicka menu screen and the last category shows your current effects. If nothing is showing there then it is a glitch.
Two solutions if it is a glitch:
a) save and restart the game
b) if glitch still occurs then just keep reverting to a previous save until you find a save that is not corrupted and your stamina regenerates.