This wasn't happening just a couple weeks ago. I have successfully used this exact MIDI keyboard with ZynAddSubFX just fine previously.
When I google this issue I find a lot of threads, all by people who just didn't understand how to connect MIDI devices in JACK or how to make sure the correct channel is selected in ZASFX's UI. I have everything connected properly AFAIK, and the issue persists.

I also saw one mention that this issue can happen with an illegimate copy of zyn-fusion, but I actually did properly purchase my copy back when it was new, and still get updates from that same source.
I may have upgraded my system since it stopped working, but I'm not sure. I don't remember installing any updates that are likely to have anything to do with this besides the linux kernel itself.