Update: Thank you soooo much for updating your post so that my answer (and the next couple) now seem to make no sense at all. If you have a different question, consider posting a different node, replying to your own node, or adding to your original node. Please don't completely change your original node. Your post gets a "--" from me.

• Open database connection
• Execute query
• Repeat step 2
• Close connection

You could see the tutorial Class::DBI Intro on the use of DBI to access a database

# code that connects to your database here

my $first_query  = $dbh->prepare('SELECT * FROM myTable');
my $second_query = $dbh->prepare('UPDATE myTable SET myField = ?');

$first_query->execute();

$second_query->bind_param(1, 'some string');
$second_query->execute();

# etc.
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MySQL server has gone away means that you're no longer connected to the server. Either you have disconnected (e.g. you've let your database handle go out of scope) or your server is dropping the connection on its end.

It's a problem you'll have to address by checking to see if the connection is alive and re-connecting as needed. One way to do this is using DBIx::Abstract:

use DBIx::Abstract;

my $dbx = DBIx::Abstract->connect(...);

sub do_query {
   $dbx->ensure_connection;
   ## do the query;
}
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$dbh = DBI->connect(...);

sub do_query {
   my $connect;
   eval { 
      ($connect) = $dbh->selectrow_array('SELECT 1');
   };
   if ($@ || !$connect) {
       $dbh = DBI->connect(...) or die "Can't reconnect: $DBI::err";  
+ 
   }

   ## do query.
}
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I do recommend DBIx::Abstract, though -- you can still get at the database handle from it, but it makes moving from MySQL to PostgresQL or Oracle a snap!

Another option: See the documentation for DBD::mysql and search for 'reconnect'.