There are several tools which you can use to help to inspect,
1. TCPmon, is a java-based tool for inspecting http call in between server and client. TCPmon also can be used to simulate slow connection.
Work mechanism of TCPmon is as a proxy. So if I describe it as below
[Your apps] ---> [tcpmon] ---> [server]
2. TCPdump, is a linux app which can be use to dump TCP connection in and out. This can be help to inspect HTTP request / HTTP come to the server.
3. Traceroute
You may want to inspect / trace connection from your server to vendor's server using traceroute, maybe the problem is in the connection.
Hope that's helpful