B737-800 pilot reported an intermittent engine fuel leak occurred on the flight; and is not an uncommon occurrence in the 737 fleet.

Narrative

After starting engines on pushback; the ground crew reported a fluid leak from the number 2 engine. In accordance with AOM; the flight crew continued to run the engine for 5 minutes. After 5 minutes; the ground crew reported that the leak did not stop; and added that it was a continuous stream. The flight crew shut down both engines; the aircraft was towed back to the gate; Maintenance was called; and a write-up was made in the logbook. The leak was reported to ATC; and airport personnel responded to clean up the fluid on the ramp. When Maintenance arrived; they requested the flight crew perform a 5-minute engine run at idle thrust on the gate. The Mechanic observed the engine for the full duration of the engine run and stated that the fluid leak had stopped. The logbook was signed off and the flight departed the gate. After pushback and engine start; the flight crew verified with the ground crew that the leak had not returned and the flight proceeded with no further incident. No abnormal indications were noted throughout the flight. Weeks later; the flight crew was informed that a passenger reported the leak continued during the taxi; and throughout the flight to ZZZ1; and that Maintenance was called to address the leak upon arrival in to ZZZ1. The crew was unaware of any leak after the initial maintenance action; or any subsequent call to Maintenance in ZZZ1 regarding a leak. The logbook shows engine oil servicing was performed in ZZZ1; but no further mention of a fluid leak on that date. The next mention of a leak in the logbook comes 8 days later referencing an R/H ENG SERVO FUEL HEATER."It is a common occurrence on the 737 to have engine fuel leaks due to faulty fuel actuators. It is company policy to fix the issue by running the engines until the fuel actuators close properly.Engine fuel leaks are all too common on the 737 fleet. It is good that specific guidance is available in the AOM; but it is concerning that fuel leaks happen so often that such guidance is necessary. It is recommended that the faulty fuel actuators be replaced with a more reliable unit instead of simply cycling them until they work. Not only would this action reduce the occurrence of fuel leaks; but also if a more serious issue arises; it will be less likely to be misdiagnosed as a typical faulty actuator."