Maybe your input signals do not contain high frequencies, but don't forget, that the MCP3202 is a fast beast! Datasheet tells, that source impedance of circuitry feeding the inputs of MPC3202 should be idealy zero Ohm. Also, the current loop area of input signal should be as minimal as possible. But you extend this area over the whole voltage divider circuitry plus multiplexer circuitry, which could add some noxious inductivity, causing an internal failure.

I don't want to say, that this is the cause of your failure, but (please don't feel offended) I see so many design rules violated in your circuit, that it is no surprise for me, that something does not work properly.

Kai