What you need to find out is HOW the load balancer is dividing up the load. Common methods are "Round Robin" which sends each new user to the next Web Server in the rotation, "Sticky IP" which sends every request from a new IP address to the next Web Server in the rotation, or true "Load Balancing" where the load on each server is monitored and requests are intelligently redirected.
With Sticky IP, you may need to do the IP Aliasing discussed above.
If you have true Load Balancing, as Roland suggested, you may just not be generating enough load for the balancer to start using a second server.
You're best bet would be to find the person(s) who configured the balancer, and have them explain to you the methods/configurations, and then have them monitor it as you execute a load test. Together, you should be able to easilly see the problem and likely the solution.