Gang:
Something that might be easy to check, to eliminate it as a possible source of the problem, is the switch. A switch with deteriorating contacts will deliver less and less voltage to the light fixtures, and flourescents don't like this.
Simply remove the switch from its mounting, remove the wires from the back (it's safe, there is only 12 volts DC here), and tie the wire ends together with a wirenut. If the lights stay on OK for longer than you previously observed them go out, the switch is probably the problem.