It could be the inductive spike that occurs when the relay turns off is greater then the LED driver board can handle. Try a non polarized small value cap across the relay contacts to help prevent the contacts from arcing and reduce the spike that occurs from turnoff.
I am very familiar wit the inrush current DC loads like coils can produce, and the diode (+resistor) that is used to divert that.
Is that also the case with light bulbs? I never had problems with the relay contacts themselves.
Strange it doesn't happen immediately, nor every time, just after a few weeks.
That maybe has to do with the momentary value of the AC voltage, at the moment it's switched off.
I have heard that in multi bulb ( incandescent) fixtures that have 3 or more bulbs in them that two of the bulbs can cause the 3rd bulb to burn out faster. Keep in mind that a incandescent bulb has inductance as well and if the florescent bulbs use a magnetic ballest that could also have a effect as well. The relay turns off the power way faster then a standard switch would so may worsen the inductive effect. The small cap would go on the AC side of the relay contacts to help reduce this effect. I would also open up the dead bulbs and see what failed on the LED driver board. I am going to guess a underrated cap or some silicon based component.
Disassemble one , for that price it is probably a capacitive mains circuit.
My guess is that the capacitor is not rated for that purpose and died taking the rest with it.
Nice example of GIGO. But we know more after the tear down.
The pcb contains a truehole little 6-pole transfo, a truehole cap and to-92 tripod (I guess transistor)
smd components are below, one 3-or-4 pole, the rest all 2-pole components.
It looks like it could be a very mainstream transfo-diodebridge-RCfilter-voltage-or-current stabilisation.
The output of a working one is 8.9V under load.
It's impossible to derive the schematic without removing the transfo.
I'll maybe do that one of the next days, maybe do some more measurements too.