Refer:
Using jQuery Autocomplete Plugin for TextBox inside Master Page in ASP.Net
I have checked the above link answer once again. Its working in all the content pages. Also i have kept the TextBox in master page. Please check your PageName where you have assigned the Url.
url: 'Default.aspx/GetAutoCompleteData',
Your Content page name will replace Default.aspx.
Check your parameter name in jQuery Ajax and WebMethod
data: "{ 'username': '" + request.term + "'}",
Both should be equal.
public static List<string> GetAutoCompleteData(string username)