Indeed, it was working for me on the front-end, but then I didn’t try the back-end.
I made a bit of a modificaiton to the plugin code, can you check if the issue is resolved now?
I suspected one function to be causing the issue, but I was not sure. On our installation the builder does not execute a part of a code, which is executed on yours, and when Ajax Search Pro tries to request it from Divi it fails.
I have added a failsafe method to prevent that, but I am not 100% sure it work. It should, but please let me know.