Cucumber Plants do not produce over and over and once the Cucumber Plant has produced all the Cucumbers it will for the season you planted them then the Cucumber Plant dies off and cannot regenerate or regrow new cucumbers.
Cucumber Plants only grow cucumbers once so if you want more cucumbers you'll need to plant new cucumber plants or cucumber seeds the next growing season.
Cucumbers are usually ready to be picked after 70 days of planting and once you've picked all the cucumbers the plant will no longer produce.