@ap I think this error might occur if the search times out.
Is the custom search configured on your application where you are seeing higher traffic or requests to the API than before?
If yes, then the most probable cause could be, you are reaching the TPS limit of your pricing tier. You can check the pricing of bing search APIs(select bing custom search API from the drop down) which mentions that the higher pricing tier has higher TPS limits.
A quick way to check if you are able to avoid this error is to update the pricing tier of your resource from azure portal and observe if it works. Thanks!!