.... i just hack at these things... but the first thing i would try is avoid the intermediary $twit, directly put it into the shared hash

 $thread_hash{'twit'}  = Net::Twitter->new(
          username => $user,
          password => $pass
    );
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.... another trick is to confine all your Twitter stuff to the thread.... is there really a need to keep a global twitter object?..... just put all the twitter stuff into the thread....

....with a sleeping thread model, as in Reusable threads demo .... and here is a Tk example with threads....notice the thread is created before any GUI code is invoked...... this goes along way toward making threaded GUI's work

#!/usr/bin/perl
use strict;
use Tk;
use threads;
use threads::shared;

my $data_out:shared = '';
my $data_in:shared = '';
my $thread_die = 0;

my $wthr = threads->new( \&update_thread )->detach;

#create Tk stuff
 my $mw = MainWindow->new(
        -background => 'black',
        -foreground => 'yellow',
        -title      => "Thread Test"
    );
    $mw->geometry("600x400");
    $mw->minsize( 400, 400 );
    $mw->maxsize( 800, 800 );

  my $sent_text = $mw->Scrolled('Text',
        -height     => 10,
        -width      => 60,
        -background => 'black',
        -foreground => 'yellow'
    )->pack( -side => 'bottom', -anchor => 's', -pady => 2 );

  my $received_text = $mw->Scrolled(
        "Text",
        -height     => 10,
        -width      => 60,
        -background => 'white',
        -foreground => 'black',
    )->pack();


my  $repeater = $mw->repeat(1000, sub{ 
    $data_out++;
    $sent_text->insert( 'end', "Sent $data_out\n" );
    $sent_text->see('end');
  
    $received_text->insert( 'end', "Received $data_in\n" );
    $received_text->see('end');
    });

$mw->Button(-text=> 'Exit',
              -command => sub{
            $thread_die = 1;
            $repeater->cancel;
                $mw->withdraw;
            kill 9, $$;
        })->pack;
MainLoop;

#########################################################
#the non-Tk worker code
sub update_thread {
    print "update_thread called...\n";
    while (1) {
          if($thread_die == 1){return}
          $data_in = 'thread-processing'.$data_out;   
      sleep 1; 
      }
}
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GUI's are notorious for having problems with threads..... another no-no with gui's is you can't manipulate the GUI (access widgets) in the main thread from the spawned thread..... Gtk2 has made a great improvement in this aspect, by the GLib::Idle_add method, which you can call from a spawned thread..... google for "glib idle_add" if interested..... Wx may have the idle_add method, since many systems use Gtk2 as the base for Wx.... but not always.