TCP Connection Limit ?

I have a UNIX program that loops while trying to make a socket connection. If the connect fails enough I run out of available TCP Connections. Here is a code fragment;
...
do {
  connected_I = -1;

    /*** OPEN SOCKET TO NT SERVER ***/
    fSocket = socket(AF_INET,SOCK_STREAM,0);
    if (fSocket == -1)
    {
      connected_I = 0;
    }

    /*** CONNECT TO SOCKET  ***/
    sin.sin_family = AF_INET;
    sin.sin_addr.s_addr = GetAddr(ip_addr);
    sin.sin_port = htons((u_short)(13011));

    if (connect(fSocket,
                (struct sockaddr FAR *) &sin,
                sizeof(sin))==-1)
    {
     connected_I = 0;
    }

    if (!connected_I)
    {
      shutdown(fSocket,2);
      close(fSocket);
      sleep(2);
    }

} while(!connected_I);
...
Can anyone see anything wrong with this?
Is there a table of some sort in UNIX that gets filled up and only released when my process terminates?
Any help anyone can offer would be great!