The following works for me:

use strict;
use warnings;

use DBI;

my $dbh = DBI->connect( "dbi:SQLite:dbname=test.sqlite", "", "", { Rai
+seError => 1 } );
$dbh->do("CREATE TABLE aaa (num INTEGER, name TEXT)");
$dbh->do("CREATE TABLE bbb (num INTEGER, name TEXT)");
my $i = 1;
for (qw(alice bob carol)) {
    $dbh->do( "INSERT INTO aaa VALUES (?, ?)", {}, $i++, $_ );
}

my $sth = $dbh->prepare("SELECT * FROM aaa");
$sth->execute;
while ( my @row = $sth->fetchrow_array ) {
    $dbh->do( "INSERT INTO bbb VALUES (?, ?)", {}, @row );
}
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Perhaps you should post the code that reproduces the problem