IIS slows down at 1000 concurrent connections

You have in fact hit one of the classic limitations of NLB. A Windows NLB cluster is only able to check if the node itself is available and cannot check if the actual application is still up and running. Ultimately what you need is for some type of health check of the application which can be done with a physical load balancer or perhaps a software load balancer such as the Microsoft Application Request Routing (ARR).

Another alternative that is somewhat new is a cloud based load balancer such as the offering from Rackspace. This gives you the benefit of having many of the features of a physical load balancer without the cost of implementing physical hardware.

Hope that helps.

Edit: There is somewhat of a way for NLB to perform health checks, however, it still requires what amounts to a third server. System Center Operations Manager has a management pack that can monitor applications. Details about that can be found here. If you are going to go through the trouble of adding something like this, you may as well look at the benefits of an actual load balancer that can perform the necessary health checks.

Can anybody provide metrics as to what are maximum Requests / sec IIS can handle?

As many as it can. You do realize that there is no limit - this basically is asking "ho fast can a car go" and the answer is "as fast as it was build for". So, requests/second says how many requests got handled per second, and that dependson how many requests came in and whether processing was fast enough - which may be cpu limited or not, depending what the cpu does.

9.75 - Active Requests

So you have only 9.75 concurrent requests at that moment in time.

Most important will likely be having a test program open that page itself and measure the time it takes to get an answer. The moment that starts taking longer you may start to develop a problem. Anything else is just a preliminary metrics, no the one you are interested in.