Just open up a new socket for your server and listen on that socket for incoming connections in an accept loop. There are examples in perlipc of both the IO::Socket and, well, non-IO::Socket variety. Just in case you don't want to use that module.

Here's the basic idea:

use IO::Socket;

my $port = 9000;

# set up a new server running on $port
my $server = IO::Socket::INET->new( Proto     => 'tcp',
                                    LocalPort => $port,
                                    Reuse     => 1)
    or die "Can't start server";

# sit in a loop and wait for connections
while ($client = $server->accept()) {
    # handle client
    # ....

    # done with client, so close up connection
    close $client;
}
[download]

Is this what you meant by "infinite"?