Hi Mel,
It is only the custom ajax handler – with the update the files are probably replaced with default server file permission, which may have been updated to not allow direct file access outside of wordpress includes and root directories.
Turning off the custom ajax handler will solve the issue. If you still getting blank (without error on live), then it also could be a miscofiguration of some sort – as the two search bars are not the same, and therefore there can be a tiny difference in the config. On the staging it works okay on my end.