sudden problem with a 3way switch
With only 1 light having a problem it is not the switch. You changed the lamps. Since it still has a problem the ballast in that fixture is failing. This is very common with electronic ballasts. When the lamps get old they stress the electronics. The lamps need to be changed as soon as they start flickering especially with black at the ends of the tubes. You will need to replace the ballast or the fixture. Some times cheaper to replace the fixture, or buy a cheap fixture of the same size and swap the ballast if it is an expensive fixture.