Okay, I might have found a solution, so far it works for me on a 3 site network, but I'm not sure if it will work 100% properly for you too.
1. Make a backup of your wp-content/plugins/ajax-search-pro folder, just in case.
2. Extract the archive attached to this post
3. There are 2 files in the extracted ajax-search-pro directory, one of them in the includes subdirectory.
4. Copy the content from the extracted ajax-search-pro directory to your server into the wp-content/plugins/ajax-search-pro folder folder. The ftp program should ask to overwrite the 2 files.
5. After copying try it.
I hope this will finally work.Best,
If you like my products, don't forget to rate them on codecanyon :)