Cucumbers are best kept at room temperature and it's not recommended to refrigerate cucumbers because they can get cold injury and not last as long in the refrigerated.
Refrigerated cucumbers will usually last from 1 to 2 weeks but if you leave the cucumbers out at room temperature they'll last for 4 to 8 weeks which is 1 to 2 months.
So if you want to make cucumbers last longer then leave them out at room temperature and they should be good to eat for at least 2 months and sometimes longer.