Thanks. I remember there has been a lot of discussion about this and I'm too tired to look it up and read it but just right to try it a bunch of times :/. It also fails for me quite a bit and I think the not switching away from the tab likely doesn't really matter it just happened to seem that way. Not sure if any of the rest of this will be useful at all.
I've found that for the best chance of success type what you want to search somewhere else and copy it then past into the search field and if it returns "no results found" then delete and paste again and repeat until it works (usually in four tries or fewer for me). In Firefox hit Ctrl-Shift-E before submitting a request to open the network monitor and watch how long timeouts take (you can leave it open while pasting and waiting; the network monitor tells you to reload but you don't need to do that; you can also deselect everything on the top row but XHR, though I'm not sure that makes much difference after the main page is loaded).
It seems almost all requests take over 15 seconds. Sometimes it takes over 30 seconds and sometime those succeed. I did get one that succeeded in just over 15 seconds as reported by Firefox (Duration column) but looking at the x-timer header (click on an entry in the network monitor to pop up info, click headers on that panel to the right and scroll down a ways) the part after VE is milliseconds that the request took and it was 14946 so just under 15 seconds.
The headers of successful requests report the server as nginx while the unsuccessful ones report varnish and a 503 response (they all go through varnish). Possibly connections are randomly closed after they have been open for a while and that might cause the failure?
If you type in the search field it can send a request for each character starting with the second (though not if you type quickly), but unfortunately it doesn't cache them if they succeed after you enter something else :(, so it is best to copy and paste and wait. It seems like it would be helpful if GOG could change the page to wait until you hit enter to search (add an icon to click too) until the underlying problem is fixed, that should at least reduce load on the system and hopefully increase the chance of success.