After more trouble-shooting, this popping sound (it is one very loud tick, that might be repeated like a crackle, or just the one, very alarming and disruptive to hear) was definitely the AES digital output, not due to any of the inputs. In our case, the problem is on an xDR-16, but I’m sure the hardware is identical for an iDR-32.
We were able to reassign the same iLive mix to an analogue output (G1 through G4, and not use that AES output) and to use that analogue output instead of the digital output and the popping has stopped, so the noise was not due to any of the inputs. The popping happened on both channels of an AES output (that is on G7 and G8 of the same XLR connector), but not on the adjacent AES output (so the G5 and G6 beside that do not have this problem).
As the AES outputs are not a plug-in card, fixing this will require removing the xDR-16 from the rack opening the unit and seeing what would need to be replaced or repaired to remedy this.