Every time I run the following program, the BrowseEntry entry comes up blank. I see no alternating behavior. The only way I can get the entry to show initial content is to uncomment the
    $midi_outdev = 'INITIAL CONTENT';
statement (update: and then I always get the same initial content :). Can you post a Short, Self-Contained, Correct Example that shows the behavior you're seeing?

c:\@Work\Perl\monks>perl
use strict;
use warnings;

use Tk;
use Tk::BrowseEntry;

my $midiCtrls = tkinit;

my @midi_outdevs = (
  'the rain in spain',
  'the cat in the hat',
  'how now brown cow',
  'foo bar baz',
  'now is the time',
  );

my $midi_outdev;
# $midi_outdev = 'INITIAL CONTENT';

my $midi_indev;

my $dropdwnMidiPort = $midiCtrls->BrowseEntry(
    -choices          => \@midi_outdevs,
    -state            => 'readonly',
    -justify          => 'right',
    -variable         => \$midi_outdev,
    -browsecmd        => sub { $midi_indev = $midi_outdev;
                   MidiConSetup('out');
                   MidiConSetup('in'); },
    -font             => 'Helvetica -12 bold',
    -disabledforeground => 'black')->grid(
    -row              => 0,
    -column           => 0);
$dropdwnMidiPort->Subwidget('slistbox')->configure(
    -selectbackground => 'IndianRed4',
    -selectforeground => 'white');

MainLoop;

exit;

sub MidiConSetup { print qq{'$_[0]' '$midi_indev' \n}; }

__END__
'out' 'how now brown cow'
'in' 'how now brown cow'
'out' 'now is the time'
'in' 'now is the time'
'out' 'the rain in spain'
'in' 'the rain in spain'
[download]

This doesn't answer your question, but it may at least provide a useful data point.