Just an idea, to maybe come closer to the problem, try to

use Data::Dumper;
[download]

somewhere early in your script and add some debugging aids into the problematic sub, like

sub get_remote_file {
      print "Retrieving data file...";
      my @site_data;
print Dumper( $conx );
      chomp( @site_data = `$conx` );
print Dumper( @site_data );
      if ( $? >> 8 ) {
        print "Failed!\n";
      } else{
        print "Success!\n";
      }
      for $line( @site_data ) {
        ( $name, $filepath, $mod, $md5 ) = split( "\,", $line );
        $site_data{$name} = ["$filepath", "$mod", "$md5"];
      }
      @site_data = ();
    }
[download]

Maybe that reveals something that would explain the different behavior of the first run compared with the subsequent ones.