Thanks for the schematic. That helps a LOT.
I don't like what I'm seeing here. But aside from that, to answer your question, the susceptibility of damage between the two voltages is not normally a considered issue only that the Zener knee of the part's Voltage/Current curve is mushier on the lower voltage. What blows the diodes since their PIVs are not the thing dying is the current thru them. The power a Zener will have to dissipate is its zener voltage x the current.
So, the current from the white wire heading to the black wire is causing power to be dissipated in the zener. So much that the zener is baking-dead. Adding a higher voltage zener could prevent the burn outs if and only if the voltage difference is higher than 2.4V but lower than 3.6V a condition I suspect is not the case.
I don't see 'noise' or 'spikes' as causing the zener's travails. More like a steady state difference between the BLACK and the WHITE wires. Often these mickey-mouse jury rigs like the zener have issues with power-up or power-down as capacitors are being charged or discharge. If the 'signal conditioner' has a bunch of capacitance then when the 28V supply is shut off that capacitance can raise the WHITE voltage above the BLACK voltage causing the capacitance to discharge thru the zener and frying it.
I'd look at the voltage across the zener during all phases of operation to see what's up; during running, power-on, and power-off periods. If it looks like the zener voltage is reached only during power-off then the scenario I described above is the likely problem. If the zener voltage is always present in all three described cases then you need to cut in an ammeter and see what's going on. If transients are suspected then you tag in a 1 ohm resistor between the top of the zener and the WHITE wire and using a scope grounded only to the WHITE wire and across the resistor you can then watch for fast large current events.
The current is the voltage/resistor. The power being dumped in the zener is that current times the zener voltage. Compare that to the allowed power of that specific zener on its data sheet.
There is also a chance this is about the other things happening on the WHITE wire coming from off to the right. Perhaps those electronics are being powered by the same 28V supply and this dumb zener scheme is being tripped up by it.
Keith Cress
kcress -