From the Streaming API documentation:
Minimize the number of connections your application makes to User Streams. Each Twitter account is limited to only a few simultaneous User Streams connections per OAuth application, regardless of IP. Once the per-application limit is exceeded, the oldest connection will be terminated. An account logging in from too many instances of the same OAuth application will cycle connections as the application instances reconnect and disconnect each other.
Per the developer policy, you should not attempt to use many applications to get around this limit. If you need a significant amount of streaming data, you should consider something like Gnip instead.