Homemade pickled vegetables will last up to 6 months.
If you pickle vegetables you should keep the jars sealed when not eating the pickled vegetables and keep them refrigerated to extend their shelf life.
You can leave the pickled vegetables out at room temperature but it's always best to just refrigerate the pickled vegetables to prevent the growth of any potential bacteria.
Refrigerating the pickled vegetables makes them last longer than if you were to just leave them out at room temperature.
If you have no room in your regular refrigerator you can buy a cheap mini fridge to store just your pickled vegetables in.