A major factor would be the number of open file descriptors the process is allowed to create. This would be true for both the server and client side.
http://redis.io/topics/clients and http://redis.io/topics/benchmarks both have the information you should work through to determine where exactly your problem is. Without the details of your setup it is unlikely we can be more specific.
Check your ulimits and your server configuration to ensure you've configured your respective systems to the limits you intend to benchmark to and you'll be able to get more usable data.