There is a way to write variables to the DATA section of your script, when the script exits, and you could store the current value there, and reread it everytime you start up, but it is cleaner to use the Inline::Files module. The hard way:

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

# The DATA filehandle is just a an open handle on the current 
# file. The current file is just the $0 variable (so long as 
# you haven't changed it)

# main part of script ...

my $count;
while(<DATA>){ $count = $_ ; print "$count\n";}
$count++;

# then redo the count update:
rewrite_count($count);

sub rewrite_count {
   my $count = shift;
   open(SELF,"+<$0")||die $!;
   while(<SELF>){last if /^__END__/}
   truncate(SELF,tell SELF);
   print SELF $count;
   close SELF;
}

__END__
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