Yes, there is a limit. The default connection limit is 2 simultaneous connections to a remote host. This can be overridden. For example, I believe that ASP.NET overrides the default value of 10 connections to the remote host by default.
From https://msdn.microsoft.com/en-us/library/7af54za5.aspx :
The number of connections between the client and server can have a significant impact on the throughput of the application. By default, an application using the HttpWebRequest class uses a maximum of two permanent connections to a specific server, but you can set the maximum number of connections for each application.
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