Today I was trying to implement an AutoCompleteExtender.
It took me a lot of time until I figured out what the problem was.
Actually the AutoCompleteExtender cannot work in a UserControl (.ascx). The only way to get the AutoCompleteExtender working is to use a service for getting the data or bring the functionality back to the Web Page itself (.aspx)
Hopefully this saves you a lot of time looking for an answer with code behind (which doesn’t exist).