currently Second Worker is calling after the complete execution of the first worker only
No, that's most certainly the wrong diagnostic. Because if that was the case then the second worker would not call req.GetResponse() until the first worker was done. So could not timeout immediately.
Something is throttling the number of concurrent http requests you can start at the same time. The server itself is certainly high on the list of candidates, particularly the kind of server that supplies the kind of data where this kind of technique makes sense. They certainly protect themselves against this. That another program can bypass this doesn't otherwise prove anything, it could do something nasty to defeat the server's detection algorithm like spoofing the IP address (I'm reaching). Lots of other candidates, like a proxy server or something silly in the anti-malware.
Do verify the server's terms of usage statement, pretty unlikely that the server owner is happy about you doing this.