I don't understand the argument here. Obviously you need some sort of amplification process to avoid noise. But there are amplifying processes that don't follow the "discrete" Shannon model. Like, I'm pretty sure neurons themselves are an example -- they maintain a stable voltage (even with noise) until they depolarize and spike. The process of depolarization is fundamentally analog, integrating together all the synaptic inputs (and anything else that affects the voltage in the cell). It can't be modeled using a sequence of discrete symbols, but it's also stable over time in the presence of noise.