First time post- take it easy on me, folks...

I'm wiring new construction in a garage, and installing 3, 96" fluorescent controlled by 3 way switches. Power source at switch #1, 3 light fixtures, then switch #2. This is a 20A circuit, with 12 gauge wiring throughout.

I ran 12-3 from switch #1 to the first fixture, then two 12-2 wires between the 3 fixtures, and then 12-3 from the last fixture to switch #2. It worked- I got light, controllable at both ends- but the lights soon started to pulse and flicker slightly.

After an hour or two, one of the fixtures failed completely (not a bulb problem)- this is the fixture furthest from switch #1 (power source).

Does this wiring scheme sound appropriate? What would cause the flickering or outright failure? Thanks for any help.