Allow me to pick some relevant bits out of your posted code and paraphrase perrin's response:

my ($dbuser, $dbpass, $dbh);

$dbuser = 'nobody';
$dbpass = 'NobodyPassword';

...
&middle_of_page();     # main content, DBI results, etc.
...

sub middle_of_page {
  # ...
  $dbh  = DBI->connect('DBI:whatever', $dbuser, $dbpass, {RaiseError =
+> 1});
  # prepare, execute and print query results
  # wrapped in HTML elements
}
[download]

Congratulations! By referencing the global "$dbh and friends" within your middle_of_page sub, you have just created a closure!

Change to

...
&middle_of_page($dbh, $dbuser, $dbpass);     # main content, DBI resul
+ts, etc.
...

sub middle_of_page {
  my ($dbh, $dbuser, $dbpass) = @_;
  # ...
  $dbh  = DBI->connect('DBI:whatever', $dbuser, $dbpass, {RaiseError =
+> 1});
  # prepare, execute and print query results
  # wrapped in HTML elements
}
[download]

and that closure will not be created, thus preventing $dbh from being preserved across calls.