Hi @robinweeda,
Apart from an AJAX error that @serafinnyc already mentioned, this can also be due to lookup tables not being set up correctly. Long story short, WooCommerce uses now a new database table to search for products, and we’ve seen problems like this happen when the update scripts for WooCommerce 3.6. and newer didn’t complete correctly.
To get this fixed, please go to WooCommerce > Status > Tools and regenerate product lookup tables on that page:
Screenshot: https://cld.wthms.co/09WNUg
It may take up to 10-15 minutes to complete, depending how many products there are in your store. If you’re still not seeing any search results after 10-15 minutes, this usually means a problem with WordPress scheduling system, so you can check with your hosting company if they can see any problems with WP Cron.
In the meantime, you can go to WooCommerce > Status > Scheduled Actions, look for Pending actions called wc_update_product_lookup_tables_column
and update the tables manually:
Screenshot: https://cld.wthms.co/EeuZGm
Cheers!