Wrap the creation of your condvars and AE::io objects in your while loop and use callbacks on the condvars instead of procedural code to do the sequential tasks, something like this:

#!/usr/bin/perl
use strict;
use warnings;

use AnyEvent;

while (1) {
        my $cv = AE::cv;
        my (@output, @input);   
        my $input_waiting = AE::cv;
        my $output_waiting = AE::cv;

        my $input_from_stdin = AE::io *STDIN, 0, sub {
                my $input = <STDIN>; # read it
                push(@input, $input);
                $input_waiting->send;
        };

        # what to do when $input_waiting has sent
        $input_waiting->cb( sub {
                push(@output, 'done');
                $output_waiting->send;
        });

        # what to do when $output_waiting has sent
        $output_waiting->cb( sub {
                print shift(@output) ."\n";
                $cv->send;
        });

        # wait for the main condvar
        $cv->recv;

}
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the while block ensures that new condvars and AE::io objects get created on each iteration of the loop. I used the simpler AE API, but that shouldn't affect the functioning of the code. You could probably get by without the $cv condvar, but it may be helpful as this is part of a larger application. You should look at the begin and end methods of AE::condvar which enables the use of single condvars as mergepoints for events, and Object::Event for a lightweight event registration and emitting library.