(CNN)A new flaw has been discovered in the computer system for the Boeing 737 Max that could push the plane downward, according to two sources familiar with the testing, an issue that is expected to further delay the aircraft's return to service.

A series of simulator flights to test new software developed by Boeing revealed the flaw, according to one of the sources.

The latest versions of Boeing's popular jet were grounded in March after two crashes -- Lion Air flight 610 and Ethiopian Airlines flight 302 -- that killed 346 people.

While the crashes remain under investigation, preliminary reports showed that a new stabilization system pushed both planes into steep nosedives from which the pilots could not recover. The issue is known in aviation vernacular as runaway stabilizer trim.

Boeing announced it could break the chain of events that led to both crashes by developing a software fix that would limit the potency of that stabilization system.

In simulator tests, government pilots discovered that a microprocessor failure could push the nose of the plane toward the ground. It is not known whether the microprocessor played a role in either crash.

When testing the potential failure of the microprocessor in the simulators, "it was difficult for the test pilots to recover in a matter of seconds," one of the sources said. "And if you can't recover in a matter of seconds, that's an unreasonable risk."