This is why there are two pilots, and techniques like Crew Resource Management dictate that one pilot be solely responsible for flying the plane while the other pilot attempts to resolve the problem.

There were a number of incidents in the 1970s where pilots got so distracted solving a problem that they let the plane crash (by running out of fuel, or by gradually descending into the ground, or several other things), so training tries to explicitly account for this problem by ensuring the pilots are very clear about who is responsible for flying and who is solving the problem, and that they clearly communicate the steps they are taking to each other.