The answer to 'why is my drain trap constantly running' is that a constantly running drain trap is typically caused by a problem with the water seal in the trap. The water seal is the U-shaped bend in the pipe that holds water and prevents sewer gases from entering the home. If the water seal is broken, it can cause the trap to constantly run as it tries to refill itself.
Some common causes of a constantly running drain trap include a cracked or damaged trap, a loose connection in the plumbing, or a blockage in the drain line. This can allow air to be sucked into the trap, causing it to constantly run in an attempt to maintain the water seal. In some cases, the drain trap may also be running due to a problem with the venting system in the home.