I've had them produce from July until frost. As long as I pick the cukes before they become pale and seedy, the plants remain productive indefinitely. Check them frequently, though  one or two that become overripe are enough to make the plant think it's succeeded in reproducing, and die.

cucumber plants in general start to flower after about 4o days from sowing seeds and continue to produce for another two months. There are many factors affecting the life expectancy of plants to produce such as weather conditions, temperature, lights, feeding, watering and plants diseases and insects infestation.