Hi David,
The issue was, that you had over 32 000 products, with a lot of content to search for (over 3 million words). The server was not able to handle the query, because of the size of the database.
Since you added back-end access, I have made a few major improvements:
– I have enabled the Index Table engine, which is specifically made for big databases like yours. It indexed 3.2 million words.
– I have changed the search logic to a much more strict one, that goes well with your number of products: https://i.imgur.com/tZuUlfP.png
– I have also enabled the custom ajax handler option, which improves the search performance by a lot
The search should respond now almost instantenously, or within a few seconds at worst.