Turns out that stuffing freshly bought cucumbers in the fridge isn't a good idea. According to UC
Davis (via Root Simple), cucumbers stored at room temperature will last much longer.
Above is a visual from UC Davis that demonstrates the levels of decay after being stored in different temperatures. Turns out that cucumbers stored for over 3 days at temperatures below 50 degrees Fahrenheit (10 Celsius) will develop what is known as "cold injury", which leads to wateriness, pitting, and faster decay.
The same tip goes for other produce like tomatoes, peppers, and eggplants too. But keep in mind that cucumbers should be kept away from the ethylene-producing tomatoes!