Cucumbers do not need to be refrigerated as long as the cucumbers have not been cut or sliced.
Once you cut or slice the cucumbers then you need to refrigerate the sliced or cut cucumbers to prevent them from going bad.
However if the cucumbers are whole cucumbers then they can stay out at room temperature and will last for up to 2 to 4 weeks.
The indoor temperature and humidity levels can affect the lifespan or shelf life of cucumbers when stored at room temperature.
I've had some cucumbers last 4 weeks and some cucumbers last only 2 weeks.
When storing the sliced cucumbers in the fridge place the sliced cucumbers in a plastic container and then place a paper towel over the top of the cucumbers to help hold in moisture of the cucumbers.
Sliced cucumbers will last in the fridge for up to 2 days or 48 hours.