Ketchup does not need refrigeration and will keep for 6 months or even longer out at room temperature after opening it.
You can refrigerate the opened bottles of ketchup to keep them fresher longer but you do not have to refrigerate ketchup for it to keep.
Ketchup is basically just tomatoes made into the ketchup and as long as you keep the ketchup bottle closed when not using it the ketchup will last for a long time.
I never refrigerate my ketchup and a lot of restaurants do not refrigerate their ketchup either.
Of course the ketchup in restaurants is used up pretty quickly but there's still no need to refrigerate ketchup unless you want too.