Voltage and temperature are the likely factors to trigger the effect at a particular time. A simple max/min reading voltmeter will show if the voltage at the fittings is dropping unusually low at the crucial time, and a digital thermometer stuck to the ballast will show if that hits an abnormal peak. The fact that it's the innermost tubes may suggest temperature, but only with a larger number of fittings (e.g 10 doing the same) would it be statistically significant. At the moment it is annoying but there haven't been enough failures to show a clear pattern.
If the voltage is marginal, then one or other ballast or tube pair that is hotter or colder might react to the low volts before the other, and this also might mean that the fitting furthest from the board is not the worst affected. Connecting a variac into the DB so that you can vary the circuit voltage would give you a chance to provoke, or avoid the effect. Even taking a fitting down and plugging it into a variac might rule out voltage effects, if you can prove that it works reliably well below the lowest voltage seen on the circuit. Sylvania technical might be able to tell you how the ballast is supposed to behave if it sees out-of-spec conditions, e.g. shut down until power-cycled, retart after 5 seconds etc.
If the voltage is not particularly low, and from your description it doesn't sound as though it will be, there might be some disturbance on the supply that these fittings are more sensitive to than anything else in the building. Only a power quality analyser will reveal that, and again there might have to be a coincidence e.g. hottest fitting + oldest tubes + power disturbance, before anything shows up.
If you can swap ballasts and tubes, it might be worth interchanging a good set with a bad one to discover whether the problem moves or remains at the same fitting. That doesn't help the customer immediately but at least gives a clue as to what step to take next. If the ballasts are ageing prematurely, and they are all from the same batch, they might all start to do it at random times over the next year or two. Sylvania have replaced the failed ones so far, probably for their own peace of mind, but may not have done a detailed analysis of the ballast internals. They might have said they can't find a problem, but there could still be a subtle failure mode that will creep up on all the fittings, such as a rogue batch of capacitors that lose performance rapidly.