Does vegetarian vegetable soup require refrigeration for food safety purposes?

It is not how "long" but more as the "temperature" of the soup. If the soup falls between the range of 41°F (5°C) - 135°F (57°C) than bacterial growth can occur. This is according to FDA Food Code. This is also a standard to any types of food!

Keep colds food COLD, and hot foods HOT!

Eat safe!