Hah. This is simple - use a hash for storing prepared statements. Untested pseudocode:

while (my $line = FILE) {
  analyze $line to extract ($table, $value) pairs
  foreach ($table, $value) pair {
    my $sql_statement = "INSERT INTO $table VALUES(?)";
    my $sth = store_or_retrieve($sql_statement);
    $sth->execute($value);
  }
}

my $sth_hashref;
sub store_or_retrieve {
   my $sql_statement = shift;
   if (exists $sth_hashref->($sql_statement)) {
      return $sth_hashref->{sql_statement;
   } else {
     my $sth = $dbh->prepare($sql_statement);
     $sth_hashref->{$sql_statement} = $sth;
     return $sth;
   }
}
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However, I would suggest you probably have more work to do regarding your database structure - do you really only have one row in each table?