That's incorrect. Electron radiation is comparably tame (though it could do the deed if a particular electron caused a spontaneous neutron emission such as what we see when Be is mixed with Po-210). Neutrons are also being radiated, and they have to go *somewhere*. The heavier your shielding, the fewer such neutrons go somewhere that interrupts your design...but no matter how thick your shielding, not all neutrons are ever fully shielded.
Neutrons that hit atoms in your wiring *will* impact your wiring, be it heat, resistence, or other potential changes. The fewer neutrons that hit your wiring, the less serious the impact, of course, but neutron emission over time increases the odds of adverse impacts.
The longer the time, the less escapes damage. This factors in to how often you replace the wiring, the electronics, the conventional explosives, the pits, the cores, and the triggers in your weapon. Certainly the less shielding that you have (e.g. a suitcase nuke), the more frequent you have to serve up high quality maintenance.
I'm well aware of the effect of neutrons. I also know that there simply aren't enough neutrons around to transmute a significant number of copper atoms to other atoms/isotopes. If there were, no human would be able to get near an atomic weapon to maintain it.
The effect certainly exists, but it is simply not significant. There are other things that will cause "wiring problems" far more quickly than neutron irradiation.
The most likely one is simply radiation damage to the insulation of the wires. I'm sure that each wire from the trigger is a "shielded wire" (can't have cross-talk among the cables from inductance as your triggering pulse is making its way to the detonators). As radiation damage accumulates in the insulation, the CAPACITANCE of that wire will change, which WILL have a major affect on the timing of your triggering pulses.