All I did was I logged in and looked at the search options, but I didn’t change a single thing. I haven’t tried it before though, so I’m not sure how that affected it.
I suspect this might be something to do with the custom ajax handler that is enabled (on the Compatibility Settings submenu). Because it is not the core ajax handler file that WordPress uses, I guess something was maybe blocking it? Perhaps some sort of optimization plugin, security plugin or server firewall or something similar. I have no clue to be honest.