Why is my bode plot showing periodic behavior?
When you are discretizing you make transformation $s \to e^{s T}$. This transforms the left half plane into unit disc. But actually it only transforms the $(-j\omega_s/2, j\omega_s/2)$ band and repeats itself by circling for outside of the band, where $\omega_s = 2 \pi / T$. This is because of the periodicity of exponential function.

When you plot the frequency response, you plot $|G(j\omega)|=|\hat{G}(e^{j\omega T})|$ for all $\omega \in [0, \infty)$ where $\hat{G}$ is the discrete transfer function. Therefore the frequency response of any sampled system is periodic.