Why don't we see new diseases more often? Or, ever?
The first thing to note is that nothing is truly new, everything is a slightly different version of what existed previously, it's only on the very long term that you can see major change. Mutations occur continuously and new variants arise often. For example you need a new flu shot every year due to the high mutation rate of the influenza virus but we still call it flu because it's only a little different.

While disease causing organisms evolve at a relatively slow rate new diseases can appear suddenly when the effect on humans suddenly changes; the most obvious example of which is when a disease changes host species. For example the sudden appearance of HIV when Simian immunodeficiency virus (SIV) "jumped species" to infect human, most likely through the consumption and processing of Primate meat. While HIV appears new it is again ancient in the sense that it has caused a similar condition to HIV/AIDS in many African non-human primates for a significant period.