It's recommended that ketchup should be kept in the fridge but in reality ketchup does not require refrigeration due to it's acidity.
It's said that you should keep ketchup in the fridge to keep it tasting good and prevent it from going bad but I've personally kept ketchup out of the fridge for years and it's never been an issue.
I use my ketchup up within a month or less anyway but I've also had ketchup that sat out for 6 months before and it was still safe to consume.
Even mustard, BBQ sauce and many other condiments do not require refrigeration.
Ketchup is pretty shelf stable and usually lasts a long time.
However the signs that ketchup have gone bad are there is a moldy surface or container, a “sour, yeasty” smell and taste, and/or a bloated container, which is a sign that the ketchup has fermented and shouldn't be consumed.
After opening condiments, you can refrigerate them for the following times: ketchup, cocktail or chili sauce 6 months.
chutney, 1 to 2 months. horseradish, 3 to 4 months.
Ketchup also becomes thicker and darker in color as it ages, more of a maroon than the bright red you traditionally think of when you picture ketchup.
They assert that a change in color with any food is a good sign that it is getting old and will taste different, so once this happens, it's time to buy a new bottle.