Homemade Hot Sauce should be kept refrigerated if not using it and the homemade hot sauce will keep for a few months in the refrigerator or you can freeze the homemade hot sauce and it will last a year or more.
Store bought hot sauce really does not require any refrigeration to keep though and will safely keep on the counter or in the pantry for 2 to 3 years before going bad.
Refrigerating the store bought hot sauce though will keep the hot sauce fresher longer and it will easily keep in the refrigerator for 3 years and sometimes longer.
Most times though people will use the hot sauce long before 3 years so there's no worry about the hot sauce going bad either way if it's left out or kept refrigerated.