There is some throttle outside of WCF (a .Net or Windows thing) that defaults to only letting a maximum of two simultaneous outbound HTTP connections. Unfortunately I can't remember for the life of me the name of the thing (and what you'd put in app.config or your app to override it). Given that you're not seeing the requests leave the client, and that it's only HTTP, I think you're hitting "that thing". I'll keep looking for its name.
Update: Found it - try this on the client (but change the '2' to a bigger number):
<configuration>
<system.net>
<connectionManagement>
<add address = "*" maxconnection = "2" />
</connectionManagement>
</system.net>
</configuration>