Summary:
If you have enabled RepliConnect API in your Web TimeSheet instance you need to make sure you have entered a valid URL under "URL of Web TimeSheet" in system preferences. If this field is blank then the a red circular icon will be displayed near the API URL field on API Request screen. Whenever you are testing a Query or you would like to run a query on your WTS database it is imperative that you enter your Web TimeSheet URL in the API URL field as the API feature would use this information to communicate with your WTS database. Attached screenshot to the solution serves as an example of this issue.

Resolution:
Make sure you have entered your Web TimeSheet URL in the API URL field.