I had no trouble getting the timeout to work properly. The connection does not get dropped. Either get() or getline() will work but I settled on get().

#!/usr/bin/perl

use strict;
use warnings;
use diagnostics;
use IO::Handle;

use Net::Telnet;

my ($host, $username, $passwd) = ("localhost", "issac", "YYYYY");

autoflush STDOUT 1;

my $t = Net::Telnet->new();

# Log into unix box
print localtime().": Connect to $host...";
my $ok = $t->open(Host    => $host,
                  Timeout => 20,
                  Errmode => "return");
die ("Cannot connect to $host telnet server") if !$ok;
print "OK\n";

print localtime().": Login to $host...";
$ok = $t->login(Name     => $username,
                Password => $passwd,
                Timeout  => 20,
                Errmode  => "return");
die ("Cannot login to $host telnet server") if !$ok;
print "OK\n";


# Read from server continually.
# Periodically send text to server.

while (1)
{
    my $output = $t->get(Timeout => 10,
                         Errmode => "return");

    if (defined $output)
    {
        # Recieved text from server
        print localtime().": get() returned definite output=\"$output\
+"\n";
    }
    elsif ($t->eof())
    {
        # End of file - server has hung up.
        print localtime().": get() returned EOF\n";
        last;
    }
    else
    {
        # Timeout occured
        print localtime().": get() returned TIMEOUT\n";

        print localtime().": put() sending string\n";
        # Send some crap to the server
        my $ok = $t->put(String => "echo HELLO\n",
                         Timeout => 10,
                         Errmode => "return");

        if (!$ok)
        {
            if ($t->eof())
            {
                print localtime().": put() returned EOF\n";
                last;
            }
            else
            {
                print localtime().": put() returned TIMEOUT\n";
            }
        }
    }
}
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Here is some sample output:

gmargo@tesla 1753$ perl  telnet_test.pl 
Thu Nov  5 19:41:00 2009: Connect to localhost...OK
Thu Nov  5 19:41:00 2009: Login to localhost...OK
Thu Nov  5 19:41:11 2009: get() returned TIMEOUT
Thu Nov  5 19:41:11 2009: put() sending string
Thu Nov  5 19:41:11 2009: get() returned definite output="echo HELLO
"
Thu Nov  5 19:41:11 2009: get() returned definite output="HELLO
issac@tesla 79$ "
Thu Nov  5 19:41:22 2009: get() returned TIMEOUT
Thu Nov  5 19:41:22 2009: put() sending string
Thu Nov  5 19:41:22 2009: get() returned definite output="echo HELLO
"
Thu Nov  5 19:41:22 2009: get() returned definite output="HELLO
issac@tesla 80$ "
Thu Nov  5 19:41:33 2009: get() returned TIMEOUT
Thu Nov  5 19:41:33 2009: put() sending string
Thu Nov  5 19:41:33 2009: get() returned definite output="echo HELLO
"
Thu Nov  5 19:41:33 2009: get() returned definite output="HELLO
issac@tesla 81$ "
Thu Nov  5 19:41:44 2009: get() returned TIMEOUT
Thu Nov  5 19:41:44 2009: put() sending string
Thu Nov  5 19:41:44 2009: get() returned definite output="echo HELLO
"
Thu Nov  5 19:41:44 2009: get() returned definite output="HELLO
issac@tesla 82$ "
[download]