wcf - Calling a Rest Service with WebClient is throwing Error

Question

Following exception is thrown when I tried to call the Rest Service from Webclient. I am Getting this exception only if I am calling this Rest service from another WCF service. If I call the Rest Service from the Console application, no error was thrown.

Here are the exception details..

{"Unable to connect to the remote server"}
    [System.Net.WebException]: {"Unable to connect to the remote server"}
    Data: {System.Collections.ListDictionaryInternal}
    HelpLink: null
    InnerException: {"A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond xxx.xxx.xx.xxx:443"}
    Message: "Unable to connect to the remote server"
    Source: "System"
    StackTrace: "   at System.Net.WebClient.UploadDataInternal(Uri address, String method, Byte[] data, WebRequest& request)\r\n   at System.Net.WebClient.UploadString(Uri address, String method, String data)\r\n   at System.Net.WebClient.UploadString(String address, String method, String data)\r\n   at 
    TargetSite: {Byte[] UploadDataInternal(System.Uri, System.String, Byte[], System.Net.WebRequest ByRef)}

Here is the Inner Exception details:

{"A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond xxx.xxx.xx.xxx:443"}
    [System.Net.Sockets.SocketException]: {"A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond xxx.xxx.xx.xxx:443"}
    Data: {System.Collections.ListDictionaryInternal}
    HelpLink: null
    InnerException: null
    Message: "A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond xxx.xxx.xx.xxx:443"
    Source: "System"
    StackTrace: "   at System.Net.Sockets.Socket.DoConnect(EndPoint endPointSnapshot, SocketAddress socketAddress)\r\n   at System.Net.Sockets.Socket.InternalConnect(EndPoint remoteEP)\r\n   at System.Net.ServicePoint.ConnectSocketInternal(Boolean connectFailure, Socket s4, Socket s6, Socket& socket, IPAddress& address, ConnectSocketState state, IAsyncResult asyncResult, Int32 timeout, Exception& exception)"
    TargetSite: {Void DoConnect(System.Net.EndPoint, System.Net.SocketAddress)} 

Any sort of Help in resolving this issue is appreciated ...