Ok, after looking into Expect a bit more, I think we've made this a bit more complicated than it needs to be. The read_all() method of Net::SSH::Expect calls the get_expect() in the same package. Per the doc, the get_expect() method will die if the Expect object does not have a valid ssh connection. So...Just wrap your call to read_all() in an eval to catch the die and you should be good. You're original code, modified in this way:

       my $ssh = Net::SSH::Expect->new (
                host => "$current_server",
                user => "$user",
                raw_pty => 1
        );

        # test the login
        eval {
                 $login_output = $ssh->run_ssh();
        };
        # I've tried to capture $@ or $! here but it never gives me an
+ything useful
        my $rc = eval{($ssh->read_all(2) =~ />\s*|$\s*\z/) or die "whe
+re's the remote prompt?";};
        unless($rc =~ /$your_expected_output_match_pattern/){
          &MOVE_ON_TO_THE_NEXT_HOST;
        }

        $ssh->exec("stty raw -echo");
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There are some other things that you should probably clean up in this example, like the poorly named $login_output and not checking the return value of the first eval (or $login_output for that matter). I'll assume you either plan to do that or were just a bit too aggressive in summarizing your code for this example.